Glossary
Every technical word in the course and what it means in plain language, with flashcards for practice.
Every technical term in the course, with a plain-language meaning. On every page these words are marked with a dotted underline: hover or tap one to see its meaning. The “Used in” links point to the sections where each term appears.
Ch 1 · Units and MeasurementCh 2 · Motion in a Straight LineCh 3 · Motion in a PlaneCh 4 · Laws of MotionCh 5 · Work, Energy and PowerCh 6 · System of Particles and Rotational MotionCh 7 · GravitationCh 8 · Mechanical Properties of SolidsCh 9 · Mechanical Properties of FluidsCh 10 · Thermal Properties of MatterCh 11 · ThermodynamicsCh 12 · Kinetic TheoryCh 13 · OscillationsCh 14 · Waves
Ch 1 · Units and Measurement
| Term | Meaning | Used in |
|---|---|---|
| absolute error | Exam extension: the magnitude of the difference between a single measurement and the mean value, $|a_i-\bar a|$. | 1.2 |
| base quantity | One of the seven independent quantities of the SI (length, mass, time, electric current, temperature, amount of substance, luminous intensity) from which all others are defined. | 1.1 1.3 |
| base unit | The unit of a base quantity: m, kg, s, A, K, mol, cd. | 1.1 1.3 7.1 |
| derived unit | A unit built from base units through the defining equation of a quantity, e.g. $1\ \text{N}=1\ \text{kg m s}^{-2}$. | 1.1 1.3 |
| dimensional analysis | Using the dimensions of quantities to check equations, convert units and deduce the form of relations between quantities. | 1.3 9.3 13.3 |
| dimensional constant | A constant of nature that has dimensions, such as $G$, $h$ or $c$ (unlike pure numbers such as $2\pi$). | 1.3 |
| dimensional equation | An equation equating a quantity's dimensions to its dimensional formula, e.g. $[v]=[\text{L}\,\text{T}^{-1}]$. | 1.3 |
| dimensional formula | The expression of a quantity in terms of the base dimensions, such as $[\text{M}\,\text{L}^2\text{T}^{-2}]$ for energy. | 1.3 5.1 6.2 7.1 |
| dimensionless quantity | A quantity with dimensions $[\text{M}^0\text{L}^0\text{T}^0]$, such as strain, an angle or a ratio of like quantities. | |
| dimensions of a quantity | The powers to which the base quantities (M, L, T, …) are raised to represent a physical quantity; e.g. force has dimensions $[\text{M}\,\text{L}\,\text{T}^{-2}]$. | 1.3 |
| exact number | A counted or defined number (20 oscillations, the 2 in $2\pi r$) with unlimited significant figures; it never limits the precision of a result. | 1.2 13.1 |
| least count | The smallest division of an instrument's scale, e.g. $1\ \text{mm}$ for a metre rule. | 1.2 8.2 |
| percentage error | Exam extension: the mean absolute error divided by the mean value, times $100\%$. | 1.2 |
| physical quantity | A measurable property of a body or process, written as a numerical value times a unit: $Q=n\,u$. | 1.1 1.3 3.1 6.2 |
| prefix | A word or symbol placed before a unit to multiply it by a power of ten, e.g. kilo (k, $10^3$), micro (µ, $10^{-6}$). | 1.1 |
| principle of homogeneity | Every term of a physically correct equation has the same dimensions. | 1.3 |
| radian | The unit of plane angle: the angle subtended at the centre of a circle by an arc equal in length to the radius; $\theta=s/r$. | 1.1 1.3 3.4 6.2 |
| rounding off | Dropping the digits beyond the significant ones; if the dropped part is exactly half, the last kept digit is made even. | 1.2 |
| scientific notation | Writing a number as $a\times10^b$ with $1\le a\lt10$; only the digits of $a$ are significant. | 1.1 1.2 |
| SI | The International System of Units, the agreed metric system used in science, built on seven base units fixed by exact values of constants of nature. | 1.1 1.3 2.1 2.2 |
| significant figures | The digits of a measured value that are known reliably, plus the first uncertain digit. | 1.1 1.2 13.1 13.2 |
| steradian | The unit of solid angle: $\Omega=A/r^2$ for a patch of area $A$ on a sphere of radius $r$; the whole sphere is $4\pi\ \text{sr}$. | 1.1 |
Ch 2 · Motion in a Straight Line
| Term | Meaning | Used in |
|---|---|---|
| acceleration due to gravity | The acceleration $g$ of a freely falling body, about $9.8\ \text{m/s}^2$ downwards near the Earth's surface; the same for all bodies at a given place. | 1.3 2.3 7.2 |
| average acceleration | Change in velocity divided by the time taken, $\bar a=\Delta v/\Delta t$; the slope of a chord of the v–t graph. | 2.2 3.1 3.3 3.4 |
| average speed | Total path length divided by the total time taken; never negative. | 2.1 2.2 2.3 3.1 |
| average velocity | Displacement divided by the time taken, $\bar v=\Delta x/\Delta t$; the slope of a chord of the x–t graph. | 2.1 2.2 2.3 3.3 |
| a–t graph | A graph of acceleration against time; the signed area under it is the change in velocity. | 2.2 |
| braking distance | The distance covered while braking from speed $u$ to rest, $\dfrac{u^2}{2|a|}$ for constant deceleration; it grows as the square of the speed. | 2.3 5.1 |
| displacement | The change in position, $\Delta x=x_2-x_1$; it has a magnitude and a direction (sign) and depends only on the start and end points. | 1.3 2.1 2.2 2.3 |
| frame of reference | A coordinate system (origin and axes) together with a clock, fixed to a chosen body, in which positions and times are measured. | 2.1 3.1 4.1 |
| free fall | Motion under gravity alone, with air resistance negligible; near the Earth the acceleration is $g=9.8\ \text{m/s}^2$ downwards for every body. | 2.3 3.3 4.3 7.2 |
| Galileo's law of odd numbers | From rest with constant acceleration, the distances covered in successive equal time intervals are in the ratio $1:3:5:7:\ldots$ | 2.3 |
| instantaneous acceleration | The rate of change of velocity at an instant, $a=dv/dt=d^2x/dt^2$; the slope of the tangent to the v–t graph. Unit $\text{m/s}^2$. | 2.2 3.4 |
| instantaneous speed | The magnitude of the instantaneous velocity, $|v|$ — the reading of a speedometer. | 2.1 |
| instantaneous velocity | The velocity at one instant, $v=\lim_{\Delta t\to0}\Delta x/\Delta t=dx/dt$; the slope of the tangent to the x–t graph. | 2.1 2.3 |
| kinematic equations | The relations $v=u+at$, $x-x_0=ut+\tfrac12at^2$, $v^2=u^2+2a(x-x_0)$ and $x-x_0=\tfrac12(u+v)t$, valid only for constant acceleration. | 1.3 2.3 3.3 |
| path length | The total length of the path actually covered (distance travelled); never negative and never less than the magnitude of the displacement. | 2.1 2.2 2.3 3.1 |
| point object | A body treated as a single point because its size is small compared with the distance it moves. | 2.1 3.3 |
| reaction time | The time between noticing a hazard and starting to act (e.g. pressing the brake); the vehicle moves at full speed during it. | 2.3 |
| relative velocity | Exam extension: the velocity of B as measured by A, $v_{BA}=v_B-v_A$ (in one dimension). | 2.3 3.3 |
| retardation | An acceleration directed opposite to the velocity, so that the body slows down (also called deceleration). | 2.2 2.3 4.1 4.2 |
| signed area | Area between a graph and the time axis, counted positive above the axis and negative below; under a v–t graph it equals $\int v\,dt$, the displacement. | 2.2 2.3 5.1 5.2 |
| stopping distance | Reaction distance plus braking distance: $d_s=ut_r+\dfrac{u^2}{2|a|}$ for constant deceleration. | 2.3 4.1 4.3 5.1 |
| uniform motion | Motion along a straight line with constant velocity; its x–t graph is a straight line. | 2.1 4.1 13.1 |
| uniformly accelerated motion | Motion in which the acceleration has the same value at every instant; its v–t graph is a straight line. | 2.3 14.2 |
| v–t graph | A graph of velocity against time; its slope is the acceleration and the signed area under it is the displacement. | 2.2 2.3 4.1 |
| x–t graph | A graph of position against time; its slope at any instant is the velocity. | 2.1 2.2 2.3 |
Ch 3 · Motion in a Plane
| Term | Meaning | Used in |
|---|---|---|
| angle of projection | The angle $\theta$ between a projectile's initial velocity and the horizontal. | 3.3 |
| angular displacement | The angle $\Delta\theta$ (in radians) through which the radius to a body turns; the arc covered is $r\,\Delta\theta$. | 3.4 13.3 |
| angular speed | The rate of turning, $\omega=\dfrac{d\theta}{dt}$, in rad/s; for uniform circular motion $\omega=\dfrac{2\pi}{T}=\dfrac vr$. | 1.3 3.4 4.4 6.2 |
| centripetal acceleration | The acceleration of a body in uniform circular motion, directed towards the centre, of magnitude $a_c=\dfrac{v^2}{r}=\omega^2r$. | 3.4 4.1 4.4 6.2 |
| complementary angles of projection | Launch angles $\theta$ and $90^\circ-\theta$; with the same speed on level ground they give the same range. | 3.3 |
| component vector | The vectors $A_x\hat{\mathbf{i}}$ and $A_y\hat{\mathbf{j}}$ along the axes whose sum is $\mathbf{A}$. | 3.2 |
| direction cosines | The cosines of the angles $\alpha$, $\beta$, $\gamma$ a vector makes with the $x$, $y$, $z$ axes: $A_x/A$, $A_y/A$, $A_z/A$; their squares add to 1. | |
| equal vectors | Vectors with the same magnitude and the same direction; an arrow may be moved parallel to itself without changing the vector. | 3.1 |
| frequency of revolution | The number of revolutions per second, $\nu=\dfrac1T$, in hertz; $\omega=2\pi\nu$. | |
| horizontal range | The horizontal distance a projectile travels before returning to its launch level, $R=\dfrac{u^2\sin2\theta}{g}$; greatest ($u^2/g$) at $45^\circ$. | 3.3 |
| law of cosines (vectors) | For two vectors at angle $\theta$ drawn tail to tail, $|\mathbf{A}+\mathbf{B}|^2=A^2+B^2+2AB\cos\theta$. | 3.2 13.1 |
| maximum height of a projectile | The greatest height above the launch level, reached when the vertical velocity is zero: $H=\dfrac{u^2\sin^2\theta}{2g}$. | 2.3 3.3 |
| parallelogram law of vector addition | Draw $\mathbf{A}$ and $\mathbf{B}$ from a common tail and complete the parallelogram; $\mathbf{A}+\mathbf{B}$ is the diagonal from the common tail. | 3.1 |
| period of revolution | The time $T$ for one complete trip round a circle; $T=\dfrac{2\pi r}{v}$. | 7.1 13.1 |
| polygon law | To add several vectors, lay them head to tail in any order; the resultant runs from the first tail to the last head. | 3.1 |
| position vector | The arrow $\mathbf{r}$ from a chosen origin to the point where a body is; it depends on the choice of origin. | 3.1 3.3 3.4 6.1 |
| projectile | A body that, once launched, moves under gravity alone; near the Earth (no air resistance) its acceleration is $g$ vertically down. | 3.3 3.4 4.1 6.1 |
| rectangular components | The signed numbers $A_x=A\cos\theta$ and $A_y=A\sin\theta$ for which $\mathbf{A}=A_x\hat{\mathbf{i}}+A_y\hat{\mathbf{j}}$; they depend on the choice of axes. | 3.2 |
| resolution of a vector | Splitting a vector into component vectors along chosen (usually perpendicular) directions. | 3.2 |
| resultant | The single vector equal to the sum of two or more vectors, $\mathbf{R}=\mathbf{A}+\mathbf{B}+\dots$ | 3.1 3.2 4.1 4.2 |
| rpm | Revolutions per minute: $1\ \text{rpm}=\tfrac1{60}\ \text{rev/s}$, so $\omega=2\pi\times\dfrac{\text{rpm}}{60}\ \text{rad/s}$. | 3.4 4.4 6.2 6.3 |
| scalar | A quantity fixed completely by a number and a unit (mass, time, speed, energy); scalars combine by ordinary arithmetic. | 3.1 3.2 |
| time of flight | The total time a projectile is in the air; on level ground $T=\dfrac{2u\sin\theta}{g}$. | 2.3 3.3 |
| trajectory | The path followed by a moving body; for a projectile it is a parabola, $y=x\tan\theta-\dfrac{gx^2}{2u^2\cos^2\theta}$. | 3.3 |
| triangle law of vector addition | Place the tail of $\mathbf{B}$ at the head of $\mathbf{A}$; $\mathbf{A}+\mathbf{B}$ runs from the tail of $\mathbf{A}$ to the head of $\mathbf{B}$. | 3.1 3.2 |
| uniform circular motion | Motion along a circle at constant speed; the velocity's direction changes continuously, so the body accelerates towards the centre. | 3.4 4.4 13.1 13.2 |
| unit vector | A vector of magnitude 1 with no unit, showing only a direction: $\hat{\mathbf{A}}=\mathbf{A}/A$; $\hat{\mathbf{i}},\hat{\mathbf{j}},\hat{\mathbf{k}}$ point along the $x$, $y$, $z$ axes. | 3.2 5.1 6.2 7.1 |
| vector | A quantity with magnitude and direction that adds by the triangle law (displacement, velocity, force); printed in bold, $\mathbf{A}$, with magnitude $A=|\mathbf{A}|$. | 2.3 3.1 3.2 3.3 |
| zero vector | The vector $\mathbf{0}$ of magnitude zero and undefined direction, e.g. $\mathbf{A}+(-\mathbf{A})$ or the displacement round a closed path. | 3.1 3.2 5.1 6.2 |
Ch 4 · Laws of Motion
| Term | Meaning | Used in |
|---|---|---|
| action–reaction pair | The two equal and opposite forces of Newton's third law; they act on different bodies, so they never cancel each other. | 4.2 7.1 |
| angle of banking | The angle $\theta$ at which a curved road is tilted; for no friction at speed $v_0$, $\tan\theta=\dfrac{v_0^2}{rg}$. | 4.4 |
| angle of repose | The largest angle of an incline on which a body stays at rest; $\tan\theta_r=\mu_s$. | 4.3 |
| apparent weight | The normal force from a supporting surface (what a scale reads), $N=m(g+a)$ with $a$ upward; zero in free fall. | 4.4 |
| Atwood machine | Two masses joined by a string over a pulley; the heavier falls with $a=\dfrac{m_1-m_2}{m_1+m_2}g$ and $T=\dfrac{2m_1m_2g}{m_1+m_2}$. | 4.4 6.1 |
| banked road | A curved road tilted so that its outer edge is higher; the normal force then leans towards the centre and helps provide the centripetal force. | 4.4 |
| centripetal force | The net force towards the centre on a body moving in a circle, $F_c=\dfrac{mv^2}{r}$; it is supplied by real forces such as tension, friction, gravity or a normal force. | 1.3 4.4 6.2 7.1 |
| coefficient of friction | The dimensionless ratio $\mu=f/N$ for a pair of surfaces: $\mu_s$ for limiting static friction, $\mu_k$ for sliding. | 4.3 4.4 5.1 5.3 |
| connected bodies | Bodies linked by strings, rods or contact so that they move with accelerations of equal size; solved with one free-body diagram per body. | 4.4 |
| conservation of linear momentum | If the net external force on a system is zero, its total momentum $m_1\mathbf{v}_1+m_2\mathbf{v}_2+\dots$ stays constant. | 4.2 5.3 6.1 |
| equilibrium of a particle | The state of zero net force, $\sum\mathbf{F}=\mathbf{0}$ (each component zero): the particle is at rest or moves with constant velocity. | 4.3 |
| external force | A force exerted on a body of a system by something outside the system; only external forces change the system's total momentum. | 4.1 4.2 5.3 6.1 |
| free-body diagram | A sketch of one body on its own with an arrow for every force acting on it (and none of the forces it exerts on other bodies). | 4.3 4.4 5.1 6.3 |
| impulse | Force times the time for which it acts, $\mathbf{J}=\mathbf{F}\,\Delta t$ (the area under a force–time graph); it equals the change in momentum. | 1.1 1.3 4.1 4.2 |
| impulsive force | A very large force acting for a very short time (a bat on a ball, a hammer blow), described by its impulse rather than its size at each instant. | 4.1 4.2 |
| inertia | The tendency of a body to resist any change in its state of rest or of uniform motion in a straight line; mass is its measure. | 4.1 4.4 6.3 7.2 |
| inertial frame of reference | A frame of reference that is not accelerating, in which Newton's laws hold; the ground is very nearly one for everyday problems. | 4.1 |
| internal force | A force exerted by one part of a chosen system on another part; internal forces cancel in pairs and cannot change the total momentum. | 4.2 6.1 6.2 8.1 |
| isolated system | A system on which the net external force is zero; its total linear momentum is constant. | 4.2 5.2 5.3 10.2 |
| kinetic friction | Friction between surfaces sliding over each other, $f_k=\mu_kN$, opposing the relative motion. | 4.3 4.4 5.1 5.2 |
| limiting friction | The maximum value of static friction, $\mu_sN$, reached when a body is just about to slide. | 4.3 |
| linear momentum | Mass times velocity, $\mathbf{p}=m\mathbf{v}$: a vector along the velocity, in kg m/s (= N s). | 4.1 4.2 6.1 6.2 |
| net force | The vector sum of all the forces acting on a body, $\mathbf{F}_\text{net}=\mathbf{F}_1+\mathbf{F}_2+\dots$; it alone determines the acceleration. | 4.1 4.2 4.3 4.4 |
| Newton's first law | A body stays at rest or in uniform motion in a straight line unless a net external force acts on it: $\mathbf{F}_\text{net}=\mathbf{0}\iff\mathbf{v}$ constant. | 4.1 |
| Newton's second law | The net external force equals the rate of change of momentum, $\mathbf{F}=\dfrac{d\mathbf{p}}{dt}$; for constant mass, $\mathbf{F}=m\mathbf{a}$. | 1.3 4.1 4.4 5.1 |
| Newton's third law | If body A exerts a force on body B, then B exerts an equal and opposite force on A: $\mathbf{F}_{AB}=-\mathbf{F}_{BA}$. The two forces act on different bodies. | 4.1 4.2 6.1 7.1 |
| normal force | The component of a contact force perpendicular to the surfaces in contact; it is as large as needed to stop one body moving into the other. | 4.2 4.3 4.4 5.1 |
| optimum speed | The speed on a banked curve at which no friction is needed, $v_0=\sqrt{rg\tan\theta}$. | 4.4 |
| recoil | The backward motion of a gun (or any body) that throws something forward; from momentum conservation, $MV=-mv$. | 4.2 |
| rolling friction | The small resistance to a wheel or ball rolling without slipping, caused by slight deformation at the contact; much smaller than sliding friction. | 4.3 5.1 |
| static friction | Friction between surfaces that are not sliding; it adjusts to oppose the tendency to slide, up to the limit $\mu_sN$. | 4.3 4.4 5.1 6.1 |
| tension | The pull exerted by a taut string, rope or cable on the bodies at its ends, directed along it; the same throughout an ideal (light, inextensible) string. | 1.3 3.2 4.3 4.4 |
| thrust | The forward force on a rocket or jet from the gas it throws backward: $F=v\,\dfrac{dm}{dt}$, where $v$ is the gas speed relative to the rocket. | 4.2 5.1 7.3 |
Ch 5 · Work, Energy and Power
| Term | Meaning | Used in |
|---|---|---|
| coefficient of restitution | For a head-on collision, $e=\dfrac{v_2-v_1}{u_1-u_2}$, the ratio of the speed of separation to the speed of approach: $1$ for elastic, $0$ for perfectly inelastic (a JEE/NEET extension). | 5.3 |
| conservative force | A force whose work between two points does not depend on the path (zero work round any closed path), e.g. gravity and the spring force; a potential energy can be defined for it. | 5.2 7.3 |
| elastic collision | A collision in which the total kinetic energy is conserved (as well as the total momentum). | 5.3 12.2 |
| elastic potential energy | The energy stored in a stretched or compressed spring, $U=\tfrac12kx^2$. | 5.2 5.3 8.2 12.3 |
| F–x graph | A graph of force against position; the signed area under it between two positions is the work done by the force. | 5.1 |
| head-on collision | A collision in which all the velocities before and after lie along one straight line (a one-dimensional collision). | 5.3 |
| horsepower | An older unit of power still used for engines: $1\ \text{hp}=746\ \text{W}$. | 5.3 |
| inelastic collision | A collision in which momentum is conserved but some kinetic energy is converted into other forms (heat, sound, deformation). | 4.2 5.3 |
| joule | The SI unit of work and energy: $1\ \text{J}=1\ \text{N m}=1\ \text{kg m}^2\text{s}^{-2}$. | 1.1 1.3 5.1 5.2 |
| kilowatt-hour | A unit of energy (the 'unit' of an electricity bill): the energy delivered in one hour at $1\ \text{kW}$, $1\ \text{kWh}=3.6\times10^6\ \text{J}$. | 1.1 5.2 5.3 6.3 |
| kinetic energy | The energy a body has because it moves: $K=\tfrac12mv^2=\dfrac{p^2}{2m}$; a scalar, never negative. | 1.3 3.4 4.2 5.1 |
| mechanical energy | The sum $E=K+U$ of kinetic and potential energies; it is constant when only conservative forces do work. | 5.2 7.3 13.2 |
| net work | The sum of the works done by all the forces on a body (equal to the work done by the resultant force). | 5.1 7.1 9.2 11.2 |
| non-conservative force | A force, such as kinetic friction or air resistance, whose work depends on the path taken; it changes the mechanical energy of a system. | 5.2 |
| perfectly inelastic collision | A collision in which the bodies stick together and move with a common velocity; the greatest loss of kinetic energy allowed by momentum conservation. | 4.2 5.3 |
| potential energy | Energy of position stored by a conservative force: $\Delta U=-W_\text{c}$. Near the Earth $U=mgh$; for a spring $U=\tfrac12kx^2$. Only changes in $U$ matter. | 5.2 5.3 7.3 8.2 |
| power (average and instantaneous) | The rate of doing work: average power $P_\text{av}=W/t$, instantaneous power $P=\dfrac{dW}{dt}=\mathbf{F}\cdot\mathbf{v}$; measured in watts. | 5.2 5.3 6.3 |
| restoring force | A force that always points back towards an equilibrium position, such as the spring force $-kx$. | 8.1 13.1 13.2 13.3 |
| scalar product | The product of two vectors that gives a scalar: $\mathbf{A}\cdot\mathbf{B}=AB\cos\theta=A_xB_x+A_yB_y+A_zB_z$; zero for perpendicular vectors. | 5.1 5.3 6.2 |
| spring constant | The stiffness $k$ of a spring: the restoring force per unit extension, $F_s=-kx$; unit $\text{N/m}$. | 1.3 5.2 8.1 13.2 |
| turning point | A position where a moving body momentarily stops and reverses, because its potential energy equals its total energy ($K=0$). | 2.1 2.2 5.2 13.2 |
| watt | The SI unit of power: $1\ \text{W}=1\ \text{J/s}$. | 1.1 5.3 10.3 |
| work done by a force | For a constant force, $W=\mathbf{F}\cdot\mathbf{d}=Fd\cos\theta$; for a variable force, the area under the $F$–$x$ graph. Positive, negative or zero; measured in joules. | 3.1 5.1 5.2 5.3 |
| work–energy theorem | The net work done on a body by all the forces acting on it equals the change in its kinetic energy, $W_\text{net}=K_f-K_i$. | 5.1 5.2 5.3 6.3 |
Ch 6 · System of Particles and Rotational Motion
| Term | Meaning | Used in |
|---|---|---|
| angular acceleration | The rate of change of angular velocity, $\alpha=d\omega/dt$, in rad/s²; the tangential acceleration of a particle is $\alpha r_\perp$. | 6.2 6.3 13.3 |
| angular momentum | The rotational analogue of momentum: for a particle $\mathbf{l}=\mathbf{r}\times\mathbf{p}$, for a body rotating about a fixed axis $L=I\omega$. Torque changes it: $d\mathbf{L}/dt=\boldsymbol\tau_\text{ext}$. | 6.2 6.3 7.1 7.3 |
| angular velocity | The rate of change of angular position, $\omega=d\theta/dt$, in rad/s; as a vector it points along the axis of rotation by the right-hand rule. A particle at distance $r_\perp$ from the axis has speed $\omega r_\perp$. | 6.2 6.3 |
| axis of rotation | The line about which a body rotates; particles on it stay at rest. | 6.1 6.3 |
| centre of gravity | The point about which the total gravitational torque on a body is zero, where its whole weight may be taken to act; in a uniform field it coincides with the centre of mass. | 6.2 |
| centre of mass | The mass-weighted average position of a system, $\mathbf{R}_\text{cm}=\sum m_i\mathbf{r}_i/M$. It moves as if all the mass were there and all the external forces acted on it: $M\mathbf{a}_\text{cm}=\mathbf{F}_\text{ext}$. | 5.2 6.1 6.2 6.3 |
| composite body | A body made of simple parts (rods, rectangles, discs); its centre of mass is found by treating each part as a particle at the part's own centre of mass, with holes counted as negative mass. | 6.1 |
| conservation of angular momentum | If the net external torque about an axis is zero, the angular momentum about it is constant: $I_1\omega_1=I_2\omega_2$, even if the body changes shape. | 6.2 7.1 |
| couple | Two equal, opposite, parallel forces with different lines of action a distance $d$ apart; zero net force but a torque $Fd$, the same about every point. | 4.2 5.3 6.2 7.1 |
| flywheel | A heavy wheel, often with most of its mass at the rim, used to store rotational kinetic energy and smooth out changes in speed. | 6.3 |
| lamina | A thin flat plate. A uniform lamina has the same thickness and density everywhere, so its centre of mass can be found using areas in place of masses. | 6.3 |
| lever arm | The perpendicular distance from the reference point (or axis) to the line of action of a force; torque = force × lever arm. | 1.3 6.2 13.3 |
| moment of inertia | The rotational inertia of a body about a given axis, $I=\sum m_ir_i^2$ with $r_i$ the perpendicular distance from the axis; unit kg m². It plays the role of mass in rotation: $K=\tfrac12I\omega^2$, $\tau=I\alpha$, $L=I\omega$. | 6.3 12.3 13.3 |
| parallel-axes theorem | $I=I_\text{cm}+Md^2$: the moment of inertia about any axis equals that about a parallel axis through the centre of mass plus $Md^2$ (JEE/NEET extension). | 6.3 |
| perpendicular-axes theorem | For a plane lamina, $I_z=I_x+I_y$ for three mutually perpendicular axes meeting at a point of the lamina, with $z$ perpendicular to its plane (JEE/NEET extension). | 6.3 |
| principle of moments | For a body in equilibrium, the sum of anticlockwise moments about any point equals the sum of clockwise moments; for a lever, load × load arm = effort × effort arm. | 6.2 |
| pure translation | Motion of a rigid body in which every particle has the same velocity at each instant; any line in the body stays parallel to itself. | 6.1 6.2 12.2 |
| radius of gyration | The distance $k$ from the axis at which the whole mass would have the same moment of inertia: $I=Mk^2$. | 6.3 |
| right-hand rule | Curl the fingers of the right hand from the first vector towards the second (or in the sense of rotation); the thumb gives the direction of the vector product (or of $\boldsymbol\omega$). | 6.2 |
| rigid body | An idealised body in which the distance between every pair of particles stays fixed, whatever forces act on it. | 4.3 6.1 6.2 6.3 |
| rolling without slipping | Rolling in which the point of contact is momentarily at rest, so $v_\text{cm}=R\omega$; the kinetic energy is $\tfrac12Mv^2+\tfrac12I_\text{cm}\omega^2$ (JEE/NEET extension). | 6.2 6.3 |
| rotation about a fixed axis | Motion of a rigid body in which one line (the axis) stays at rest and every other particle moves in a circle centred on that line, in a plane perpendicular to it. | 6.1 6.3 |
| rotational kinetic energy | The kinetic energy of a body rotating about an axis, $K=\tfrac12I\omega^2$. | 6.3 12.3 |
| system of particles | A collection of particles considered together, such as a rigid body, a gas or two colliding balls; forces between its members are internal. | 6.1 6.2 |
| torque | The turning effect of a force about a point, $\boldsymbol\tau=\mathbf{r}\times\mathbf{F}$, of magnitude $rF\sin\theta$ = force × lever arm; unit N m. | 1.3 4.3 6.2 6.3 |
| vector product | The product $\mathbf{A}\times\mathbf{B}$: a vector of magnitude $AB\sin\theta$, perpendicular to both $\mathbf{A}$ and $\mathbf{B}$ by the right-hand rule. It is not commutative: $\mathbf{B}\times\mathbf{A}=-\mathbf{A}\times\mathbf{B}$. | 6.2 |
Ch 7 · Gravitation
| Term | Meaning | Used in |
|---|---|---|
| aphelion | The point of an orbit farthest from the Sun, at distance $a(1+e)$; the body moves slowest there. | 7.1 |
| areal velocity | The rate at which the line from the Sun to a planet sweeps out area, $\tfrac12rv_\perp=L/2m$; constant by Kepler's second law. | 7.1 |
| binding energy of a satellite | The energy that must be supplied to free an orbiting satellite completely: $GMm/2r$ for a circular orbit of radius $r$. | 7.3 |
| binomial approximation | For small $x$, $(1+x)^n\approx1+nx$; e.g. $(1+h/R)^{-2}\approx1-2h/R$. | 7.2 14.2 |
| bound and unbound | A body is bound to a planet if its total energy $E=K+U$ is negative (it cannot escape) and unbound if $E\ge0$. | 7.3 |
| central force | A force always directed towards (or away from) a fixed point; it exerts no torque about that point, so angular momentum about it is conserved. | 6.2 7.1 |
| eccentricity | A number $e=c/a$ between 0 and 1 measuring how stretched an ellipse is: $e=0$ is a circle. | 7.1 |
| escape speed | The least launch speed from a planet's surface for a body never to return: $v_e=\sqrt{2GM/R}=\sqrt{2gR}$, about $11.2\ \text{km/s}$ for the Earth. | 1.3 7.3 12.2 |
| geostationary satellite | A satellite in a circular equatorial orbit with a 24-hour period, about $36\,000\ \text{km}$ up, which stays above one point of the Earth (beyond the board syllabus). | 7.3 |
| gravimeter | A very sensitive instrument that measures small differences in $g$ from place to place, used in geology and surveying. | 7.2 13.3 |
| gravitational constant | The constant $G=6.67\times10^{-11}\ \text{N m}^2\,\text{kg}^{-2}$ in Newton's law of gravitation; the same everywhere in the universe. | 1.3 7.1 |
| gravitational field strength | The gravitational force per unit mass at a point, $g=F/m$, in $\text{N/kg}$ (the same as $\text{m/s}^2$); a vector pointing towards the attracting mass. | 7.2 |
| gravitational potential | Gravitational potential energy per unit mass at a point, $V=-GM/r$ outside a sphere of mass $M$; unit $\text{J/kg}$. | 7.3 |
| gravitational potential energy | For masses $M$ and $m$ a distance $r$ apart, $U=-GMm/r$, taking $U=0$ at infinite separation; near the Earth's surface its changes reduce to $mgh$. | 5.2 7.3 9.2 9.3 |
| Kepler's laws | Three rules of planetary motion: orbits are ellipses with the Sun at a focus; the Sun–planet line sweeps equal areas in equal times; $T^2\propto a^3$. | 1.3 7.1 |
| orbital speed | The speed of a satellite in a circular orbit of radius $r$: $v_o=\sqrt{GM/r}$; about $7.9\ \text{km/s}$ just above the Earth. | 3.4 7.1 7.3 |
| perihelion | The point of a planet's (or comet's) orbit nearest the Sun, at distance $a(1-e)$; the body moves fastest there. | 7.1 |
| satellite | A body orbiting a planet, natural (the Moon) or artificial; gravity provides its centripetal force. | 1.3 3.4 7.1 7.2 |
| semi-major axis | Half the longest diameter of an ellipse, $a$; for an orbit, the average of the perihelion and aphelion distances. | 7.1 |
| spherically symmetric | Describes a body whose density depends only on the distance from its centre; outside, it attracts as if all its mass were at the centre. | 7.2 7.3 |
| torsion balance | A rod hung from a fine wire, whose tiny twist measures very small forces; used by Cavendish to measure $G$. | 7.1 |
| uniform-Earth model | Treating the Earth as a sphere of constant density; it gives $g(d)=g(1-d/R_E)$ below the surface. | 7.2 |
| universal law of gravitation | Every two particles attract with a force $F=Gm_1m_2/r^2$ along the line joining them. | 3.4 7.1 7.2 7.3 |
Ch 8 · Mechanical Properties of Solids
| Term | Meaning | Used in |
|---|---|---|
| bulk modulus | The ratio of hydraulic stress to volume strain, $B=-\dfrac{p}{\Delta V/V}$, positive because the volume falls as the pressure rises; unit Pa. Defined for solids, liquids and gases. | 8.1 8.2 9.1 14.1 |
| compressibility | The reciprocal of the bulk modulus, $k=1/B$: the fractional decrease in volume per unit increase in pressure; unit Pa⁻¹. | 8.2 |
| ductile | Describes a material with a large plastic region between the elastic limit and fracture, so it can be drawn into wires and stretches before breaking (copper, gold, mild steel). Opposite: brittle (glass, cast iron). | 8.1 |
| elastic limit | The greatest stress at which a body still returns completely to its original size and shape when unloaded (the yield point); beyond it the body is left with a permanent set. | 5.2 8.1 8.2 |
| elasticity | The property of a body by which it regains its original size and shape when the deforming force is removed. In physics, the material with the larger modulus (larger restoring stress for the same strain) is called the more elastic — steel is more elastic than rubber. | 5.3 8.1 12.2 14.1 |
| Hooke's law | Within the proportional limit, stress is directly proportional to strain: stress = modulus of elasticity × strain. For a spring or wire, $F=k\,\Delta L$. | 5.2 8.1 8.2 10.1 |
| lateral strain | The fractional change in width or diameter, $\Delta d/d$, that accompanies a longitudinal strain; negative when the body is stretched. | 8.2 |
| modulus of elasticity | The ratio stress/strain in the region where Hooke's law holds; unit Pa. A property of the material, not of the specimen's size or shape: Young's, shear and bulk moduli for the three kinds of deformation. | 8.1 8.2 |
| plasticity | The property of a body by which it does not regain its original size and shape when the deforming force is removed, so the deformation is permanent (putty, wet clay; metals beyond their elastic limit). | 8.1 |
| Poisson's ratio | Lateral strain divided by longitudinal strain, with a minus sign: $\nu=-\dfrac{\Delta d/d}{\Delta L/L}$. Dimensionless; about 0.2–0.4 for metals, nearly 0.5 for rubber, and never above 0.5 for ordinary materials. | 8.2 |
| proportional limit | The greatest stress up to which stress is proportional to strain — the end of the straight part of the stress–strain curve. | 8.1 8.2 10.1 |
| Searle's method | A laboratory method for Young's modulus: an experimental wire and a reference wire hang from one support; a spirit level and micrometer measure the extension, and $Y=\dfrac{L}{A}\times$ (slope of the load–extension graph). | 8.2 |
| shear modulus | The ratio of shearing stress to shearing strain, $G=\dfrac{F}{A\theta}$ (the modulus of rigidity); unit Pa. Only solids have one; for most solids it is roughly a third to two fifths of $Y$. | 8.1 8.2 14.1 |
| strain | The fractional change in size or shape caused by a stress: longitudinal $\Delta L/L$, shearing $\Delta x/L\approx\theta$, or volume $\Delta V/V$. A pure number with no unit. | 1.3 8.1 8.2 9.3 |
| stress | The restoring force per unit area that develops inside a deformed body, equal in magnitude to $F/A$; unit Pa (N/m²). Longitudinal (tensile or compressive), shearing (tangential) or hydraulic (equal to the fluid pressure). | 1.1 1.3 6.2 6.3 |
| ultimate tensile strength | The greatest stress a material can withstand in tension (the highest point of its stress–strain curve). A wire of cross-section $A$ has breaking load $\sigma_uA$. | 8.1 |
| Young's modulus | The ratio of longitudinal (tensile or compressive) stress to longitudinal strain within the proportional limit, $Y=\dfrac{FL}{A\,\Delta L}$; unit Pa. About $2.0\times10^{11}$ Pa for steel. | 8.1 8.2 10.1 14.2 |
Ch 9 · Mechanical Properties of Fluids
| Term | Meaning | Used in |
|---|---|---|
| absolute pressure | The total pressure at a point, including atmospheric pressure: $p=p_a+\rho gh$ at depth $h$ in an open liquid. | 9.1 9.2 12.1 |
| angle of contact | The angle between a solid surface and the tangent to the liquid surface where they meet, measured through the liquid; below $90^\circ$ the liquid wets the solid. | 9.4 |
| atmospheric pressure | The pressure of the air at a place, about $1.013\times10^5\ \text{Pa}$ (1 atm, 76 cm of mercury) at sea level. | 9.1 9.2 9.4 10.1 |
| barometer | An instrument that measures atmospheric pressure; in a mercury barometer $p_a=\rho_\text{Hg}gh$ with $h\approx76\ \text{cm}$ at sea level. | 9.1 9.4 |
| Bernoulli's principle | Along a streamline in steady flow of an ideal fluid, $p+\tfrac12\rho v^2+\rho gh$ is constant — conservation of energy per unit volume. | 9.2 9.3 |
| capillary rise | The rise (or fall) of a liquid in a narrow tube caused by surface tension: $h=\dfrac{2S\cos\theta}{\rho gr}$. | 9.4 |
| coefficient of viscosity | The constant $\eta$ in $F=\eta A\dfrac{dv}{dx}$: viscous force per unit area per unit velocity gradient; unit $\text{Pa s}$, dimensions $[\text{M L}^{-1}\text{T}^{-1}]$. | 9.3 |
| cohesion and adhesion | Cohesion is the attraction between molecules of the same substance; adhesion is the attraction between molecules of different substances, such as a liquid and a solid. | 9.4 |
| dynamic lift | The force on a body moving through a fluid when the flow is faster on one side, so the pressure there is lower — the lift on a wing, or the swerve of a spinning ball (Magnus effect). | 9.2 |
| equation of continuity | For steady flow of an incompressible fluid, $A_1v_1=A_2v_2$: the speed is greatest where the cross-section is smallest (conservation of mass). | 9.2 |
| excess pressure | The amount by which the pressure inside a curved liquid surface exceeds that outside: $2S/r$ for a drop or an air bubble in a liquid, $4S/r$ for a soap bubble. | 9.4 13.1 14.4 |
| fluid | A substance that flows — it cannot resist a shearing stress while at rest. Liquids and gases are fluids. | 1.3 4.3 8.1 8.2 |
| gauge pressure | The excess of the absolute pressure over atmospheric pressure, $p-p_a$; at depth $h$ in an open liquid it is $\rho gh$. | 9.1 9.2 12.1 |
| hydraulic machine | A device in which a small force on a small piston produces a large force on a large piston through an enclosed liquid: $F_2=\dfrac{A_2}{A_1}F_1$. | 8.2 9.1 |
| hydrostatic paradox | The pressure at the base of a vessel depends only on the depth of liquid, not on the vessel's shape or the amount of liquid it holds. | 9.1 |
| laminar flow | Flow in which the fluid moves in smooth layers that slide over one another without mixing. | 9.3 |
| manometer | A U-tube containing a liquid, used to measure a gauge pressure from the difference $h$ in its levels: $p-p_a=\rho gh$. | 9.1 9.2 |
| meniscus | The curved surface of a liquid in a narrow tube: concave if the liquid wets the tube ($\theta\lt90^\circ$), convex if it does not. | 9.4 |
| Pascal's law | In a fluid at rest the pressure at a point is the same in all directions and the same at all points at one level; a pressure change applied to an enclosed fluid is transmitted undiminished throughout it. | 9.1 |
| poise | The CGS unit of viscosity: $1\ \text{poise}=0.1\ \text{Pa s}$. | 9.3 |
| relative density | The density of a substance divided by the density of water ($1.00\times10^3\ \text{kg/m}^3$); a pure number. | 1.3 9.1 |
| Reynolds number | The dimensionless number $Re=\dfrac{\rho vd}{\eta}$ that decides whether flow in a pipe is laminar (below about $1000$) or turbulent (above about $2000$). | 9.2 9.3 |
| speed of efflux | The speed $v=\sqrt{2gh}$ of liquid leaving a small hole a depth $h$ below the free surface of a wide open tank (Torricelli's law). | 9.2 |
| Stokes' law | The viscous drag on a small sphere moving slowly through a fluid: $F=6\pi\eta rv$ (laminar flow round the sphere). | 1.3 9.3 |
| streamline | The path of a fluid particle in steady flow; the fluid velocity is along its tangent at every point, and two streamlines never cross. | 9.2 |
| streamline flow | Flow in which the velocity of the fluid at each fixed point does not change with time, so particles passing a point all follow the same path. | 9.2 |
| surface energy | The extra energy of the molecules in a liquid's surface; increasing the area by $\Delta A$ needs work $S\,\Delta A$. | 9.4 |
| surface tension | The force per unit length acting across a line in a liquid surface, in the plane of the surface: $S=F/l$, unit $\text{N/m}$. It equals the surface energy per unit area. | 1.3 9.4 12.1 14.1 |
| surfactant | A substance, such as a detergent, that gathers at a liquid surface and lowers its surface tension, helping the liquid to spread and wet. | 9.4 |
| terminal velocity | The constant velocity a body reaches when falling through a fluid, when drag balances weight minus upthrust; for a small sphere $v_t=\dfrac{2r^2(\rho-\sigma)g}{9\eta}$. | 4.1 9.3 |
| tube of flow | A bundle of streamlines through a small area; fluid never crosses its sides, so it behaves like a pipe. | 9.2 |
| turbulent flow | Irregular flow in which the velocity at a point fluctuates with eddies and swirls; it sets in above a critical speed. | 9.2 9.3 |
| upthrust | The upward force of a fluid on an immersed body, equal to the weight of fluid displaced (Archimedes' principle). | 9.1 9.3 12.1 |
| velocity gradient | The rate of change of flow speed with distance at right angles to the flow, $\dfrac{dv}{dx}$; unit $\text{s}^{-1}$. | 9.3 |
| Venturi meter | A pipe with a narrow throat; the pressure drop at the throat, with continuity and Bernoulli's principle, gives the flow speed and flow rate. | 9.2 |
| viscosity | The internal friction of a fluid: the resistance of its layers to sliding over one another. | 1.3 9.1 9.2 9.3 |
| volume flow rate | The volume of fluid crossing a section per second, $Q=Av$; unit $\text{m}^3\text{/s}$. | 9.2 |
Ch 10 · Thermal Properties of Matter
| Term | Meaning | Used in |
|---|---|---|
| absolute zero | The lowest possible temperature, $0\ \text{K}=-273.15\ ^\circ\text{C}$, at which an ideal gas would exert no pressure. It can be approached but never reached. | 10.1 11.3 12.1 12.2 |
| anomalous expansion of water | The unusual behaviour of water, which contracts when heated from $0\ ^\circ\text{C}$ to about $4\ ^\circ\text{C}$ and expands only above that; its density is greatest at $4\ ^\circ\text{C}$, which is why lakes freeze from the top down. | 10.1 |
| bimetallic strip | Two strips of metals with different expansion coefficients (e.g. brass and steel) joined along their length. A temperature change makes it curl, with the metal of larger $\alpha$ on the convex side when heated; used in thermostats and dial thermometers. | 10.1 |
| blackbody | An ideal body that absorbs all radiation falling on it at every wavelength; it is also the best possible emitter at any temperature (emissivity $e=1$). A small hole in a hollow enclosure is a good approximation. | 10.3 |
| boiling point | The temperature at which a liquid boils, its vapour pressure equalling the pressure above it; the normal boiling point is at 1 atm ($100\ ^\circ\text{C}$ for water). It rises with pressure (about $120\ ^\circ\text{C}$ in a pressure cooker) and falls at altitude. | 10.1 10.2 |
| calorimeter | A thermally insulated vessel (usually thin polished copper with a stirrer, lid and outer jacket) in which heats are measured by mixing bodies and recording temperatures. | 10.2 12.3 |
| coefficient of linear expansion | The fractional increase in length per kelvin, $\alpha=\dfrac{\Delta L}{L\,\Delta T}$; unit $\text{K}^{-1}$. About $1.2\times10^{-5}\ \text{K}^{-1}$ for steel. For an isotropic solid the area and volume coefficients are $2\alpha$ and $3\alpha$. | 10.1 |
| coefficient of volume expansion | The fractional increase in volume per kelvin, $\gamma=\dfrac{\Delta V}{V\,\Delta T}$; unit $\text{K}^{-1}$. Of order $10^{-5}$ for solids, $10^{-4}$–$10^{-3}$ for liquids and $1/T$ for an ideal gas at constant pressure. | 10.1 |
| conduction (of heat) | Transfer of heat through a material from hotter to colder parts without any bulk movement of the material, by vibrating atoms passing energy to their neighbours (and, in metals, by free electrons). | 10.2 10.3 11.3 |
| constant-volume gas thermometer | A thermometer that measures temperature by the pressure of a fixed volume of gas at low density: $T=273.16\ \text{K}\times p/p_\text{tp}$. Extrapolating its straight-line graph to zero pressure locates absolute zero. | 10.1 |
| convection | Transfer of heat by the bulk movement of a fluid carrying its energy with it. In natural convection, warmer, less dense fluid rises under gravity and cooler fluid sinks; in forced convection a fan or pump drives the flow. | 10.1 10.2 10.3 12.3 |
| emissivity | The ratio $e$ ($0\le e\le1$) of the power radiated by a surface to that radiated by a blackbody of the same area and temperature. Good absorbers have high emissivity; polished metals have low emissivity. | 10.3 |
| heat capacity | The heat needed to raise the temperature of a particular body by one kelvin, $S=\Delta Q/\Delta T$; unit J/K. It equals $mc$ for a body of mass $m$ made of one material. | 10.2 10.3 11.1 12.3 |
| ideal-gas equation | $pV=nRT$, relating the pressure, volume, absolute temperature and number of moles of a gas at low density, with $R=8.31\ \text{J mol}^{-1}\text{K}^{-1}$. A gas obeying it exactly is an ideal gas. | 10.1 12.1 |
| kelvin scale | The SI temperature scale, measured from absolute zero in steps the same size as the Celsius degree: $T=t_C+273.15$. Its unit is the kelvin, K (no degree sign); it is the scale to use in every formula containing $T$ itself. | 10.1 10.3 11.3 12.1 |
| latent heat | The heat absorbed or given out per unit mass during a change of state at constant temperature, $L=Q/m$; unit J/kg. For water $L_f=3.33\times10^5\ \text{J/kg}$ (fusion) and $L_v=2.26\times10^6\ \text{J/kg}$ (vaporisation). | 10.2 11.1 11.2 |
| melting point | The temperature at which the solid and liquid states of a substance coexist in equilibrium at a given pressure; the normal melting point is at 1 atm ($0\ ^\circ\text{C}$ for ice). For ice it falls slightly as the pressure rises. | 10.2 |
| molar specific heat capacity | The heat capacity per mole, $C=\dfrac{1}{n}\dfrac{\Delta Q}{\Delta T}=Mc$; unit $\text{J mol}^{-1}\text{K}^{-1}$. About $3R\approx25\ \text{J mol}^{-1}\text{K}^{-1}$ for most metals at room temperature; for gases it depends on the conditions ($C_p$, $C_v$). | 10.2 11.2 12.3 |
| Newton's law of cooling | For a small temperature excess over the surroundings, the rate of loss of heat is proportional to the excess: $\dfrac{dT}{dt}=-k(T-T_s)$, giving $T-T_s=(T_0-T_s)e^{-kt}$. | 10.3 |
| principle of calorimetry | In a thermally isolated system, the heat lost by the hotter bodies equals the heat gained by the colder ones: $\sum m_ic_i(T_f-T_i)=0$ (plus $mL$ terms for any change of state). The basis of the method of mixtures. | 10.2 12.3 |
| regelation | The melting of ice under pressure and its refreezing when the pressure is removed, as when a loaded wire passes through a block of ice, which stays in one piece. | 10.2 |
| specific heat capacity | The heat needed per unit mass per unit rise in temperature, $c=\dfrac{1}{m}\dfrac{\Delta Q}{\Delta T}$, so that $Q=mc\,\Delta T$; unit $\text{J kg}^{-1}\text{K}^{-1}$. $4186\ \text{J kg}^{-1}\text{K}^{-1}$ for liquid water. | 10.2 10.3 11.2 12.3 |
| Stefan–Boltzmann law | The power radiated by a body of area $A$ and emissivity $e$ at absolute temperature $T$ is $P=e\sigma AT^4$, with $\sigma=5.67\times10^{-8}\ \text{W m}^{-2}\text{K}^{-4}$; the net loss to surroundings at $T_s$ is $e\sigma A(T^4-T_s^4)$. | 10.3 |
| sublimation | A change of state directly from solid to vapour (or the reverse) without passing through the liquid state, as with camphor, iodine and solid carbon dioxide. | 10.2 |
| thermal conductivity | The constant $K$ in $H=KA\dfrac{T_1-T_2}{L}$ for steady conduction through a slab; unit $\text{W m}^{-1}\text{K}^{-1}$. About $385$ for copper, $0.8$ for glass and $0.024$ for still air. | 10.3 |
| thermal radiation | Electromagnetic radiation (mostly infrared at everyday temperatures) emitted by every body because of the thermal motion of its charged particles; it needs no medium and crosses a vacuum at the speed of light. | 10.3 |
| thermal resistance | $R=\dfrac{L}{KA}$ for a slab of thickness $L$, area $A$ and conductivity $K$, so that $H=\Delta T/R$; unit K/W. Resistances of slabs in series add, as for electrical resistors. | 10.3 |
| thermal stress | The stress in a body that is prevented from expanding or contracting freely when its temperature changes; for a rod clamped between rigid supports $\sigma=Y\alpha\,\Delta T$, independent of its length. | 10.1 14.2 |
| triple point of water | The unique temperature and pressure at which ice, liquid water and water vapour coexist in equilibrium; assigned the value $273.16\ \text{K}$ ($0.01\ ^\circ\text{C}$) to fix the kelvin scale. | 10.1 10.2 |
| Wien's displacement law | The wavelength at which a blackbody's emission peaks is inversely proportional to its absolute temperature: $\lambda_mT=b=2.9\times10^{-3}\ \text{m K}$. Hotter bodies glow bluer. | 10.3 |
Ch 11 · Thermodynamics
| Term | Meaning | Used in |
|---|---|---|
| adiabatic process | A process with no exchange of heat ($Q=0$), so $\Delta U=-W$. For a quasi-static adiabatic change of an ideal gas $pV^\gamma=$ constant. | 11.2 11.3 |
| adiabatic wall | A boundary that allows no heat to flow through it — a perfect insulator, such as the evacuated double wall of a vacuum flask. Work can still be done through it if it moves. | 11.1 |
| Carnot engine | An ideal reversible engine whose gas runs through two isothermal and two adiabatic steps between a source at $T_1$ and a sink at $T_2$; its efficiency $1-T_2/T_1$ is the greatest possible between those temperatures. | 11.3 |
| Clausius statement | No process is possible whose sole result is the transfer of heat from a colder object to a hotter object. | 11.3 |
| coefficient of performance | For a refrigerator, $\beta=Q_2/W$, the heat removed from the cold space per unit work done on it; at most $T_2/(T_1-T_2)$. A heat pump is rated by $Q_1/W$. (Exam extension.) | 10.3 11.2 11.3 |
| diathermic wall | A boundary that lets heat flow freely between the systems on either side, such as a thin copper sheet. | 11.1 |
| efficiency of a heat engine | A heat engine works in a cycle, taking heat $Q_1$ from a source, doing work $W$ and rejecting $Q_2$ to a sink; its efficiency is $\eta=W/Q_1=1-Q_2/Q_1$, always less than 1. | 11.3 |
| equation of state | The relation between the state variables of a system in equilibrium; for an ideal gas, $pV=nRT$. | 11.2 |
| extensive and intensive variables | An extensive variable ($V$, $n$, mass, $U$) doubles when the system is doubled; an intensive one ($p$, $T$, density) does not. | |
| first law of thermodynamics | Energy conservation for heat and work: $\Delta U=Q-W$, where $Q$ is the heat supplied to the system and $W$ the work done by the system. | 11.1 |
| free expansion | The expansion of a gas into a vacuum inside insulated walls: $Q=0$, $W=0$, $\Delta U=0$, so the temperature of an ideal gas is unchanged. It is not quasi-static and is irreversible. | 10.1 11.3 |
| heat reservoir | A body so large that it can give out or absorb any amount of heat without its temperature changing; the hotter one used by an engine is the source, the colder one the sink. | 11.3 |
| internal energy | The total kinetic and potential energy of the molecules of a system, measured in the frame in which the system is at rest; a property of the state, $U$. For an ideal gas it depends only on the temperature. | 11.1 11.2 11.3 12.2 |
| irreversible process | Any process that cannot be exactly undone without leaving a change in the surroundings — e.g. free expansion, heat flow across a finite temperature difference, friction. All natural processes are irreversible. | 11.3 |
| isobaric process | A process at constant pressure: $W=p\,\Delta V=nR\,\Delta T$ and $Q=nC_p\,\Delta T$ for an ideal gas. | 11.2 14.2 |
| isochoric process | A process at constant volume: no work is done, and all the heat changes the internal energy, $Q=\Delta U=nC_v\Delta T$. | 11.2 14.2 |
| isothermal process | A process at constant temperature. For an ideal gas $pV=$ constant, $\Delta U=0$ and $Q=W=nRT\ln(V_2/V_1)$. | 11.1 11.2 11.3 14.2 |
| Kelvin–Planck statement | No process is possible whose sole result is the absorption of heat from a reservoir and the complete conversion of this heat into work. | 11.3 |
| molar specific heats at constant volume and pressure | $C_v$ and $C_p$: the heat needed to raise the temperature of one mole of a gas by $1\ \text{K}$ with its volume, or its pressure, held fixed. For an ideal gas $C_p-C_v=R$ (Mayer's relation). | 11.2 |
| p–V diagram | A graph of the pressure of a gas against its volume, on which each equilibrium state is a point and a quasi-static process is a curve; the area under the curve is the work done by the gas. | 11.1 11.2 |
| quasi-static process | An idealised, infinitely slow process in which the system passes through a continuous sequence of equilibrium states, so it can be drawn as a curve on a $p$–$V$ diagram. | 11.2 11.3 |
| ratio of specific heats | $\gamma=C_p/C_v$, greater than 1: $\tfrac53$ for a monatomic ideal gas and $\tfrac75$ for a diatomic one such as air. | 10.2 11.2 14.2 |
| reversible process | A process that can be run backwards so that both the system and its surroundings return exactly to their initial states; it must be quasi-static and free of friction and other dissipation. | 11.3 |
| second law of thermodynamics | The law that fixes the direction of natural processes: no cyclic device can turn heat from one reservoir completely into work (Kelvin–Planck), and heat cannot flow by itself from a colder to a hotter body (Clausius). | 11.3 |
| state variable | A macroscopic quantity ($p$, $V$, $T$, $n$, $U$) whose value depends only on the present equilibrium state of a system, not on how it got there. Heat and work are not state variables. | 11.2 |
| thermal equilibrium | The condition of two systems in diathermic contact when no net heat flows between them and neither state changes; systems in thermal equilibrium have the same temperature. | 10.1 11.1 12.3 |
| thermodynamic system | The part of the universe chosen for study (a gas in a cylinder, water in a kettle); everything outside it that can exchange energy with it is its surroundings. | 11.1 |
| zeroth law of thermodynamics | If two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other. It makes temperature a well-defined property and is the basis of thermometers. | 11.1 |
Ch 12 · Kinetic Theory
| Term | Meaning | Used in |
|---|---|---|
| Avogadro constant | The number of elementary entities (atoms or molecules) in one mole, $N_A=6.02\times10^{23}\ \text{mol}^{-1}$. | 1.1 12.1 |
| Avogadro's hypothesis | Equal volumes of all gases at the same temperature and pressure contain the same number of molecules; it follows from $pV=Nk_BT$. | 12.1 |
| Boltzmann constant | The gas constant per molecule, $k_B=\dfrac{R}{N_A}=1.38\times10^{-23}\ \text{J/K}$; it appears in $pV=Nk_BT$ and in the mean kinetic energy of a molecule, $\tfrac32k_BT$. | 1.1 12.1 |
| Boyle's law | For a fixed amount of gas at constant temperature, $pV$ is constant: halving the volume doubles the pressure. | 10.1 11.2 12.1 |
| Brownian motion | The ceaseless irregular jiggling of small particles suspended in a liquid or gas, caused by uneven bombardment by the fluid's molecules — direct evidence of molecular motion. | 12.1 |
| Charles's law | For a fixed amount of gas at constant pressure, the volume is proportional to the absolute temperature: $\dfrac{V_1}{T_1}=\dfrac{V_2}{T_2}$. | 10.1 12.1 |
| collision frequency | The average number of collisions a gas molecule makes per second, about $\dfrac{v}{\lambda}$; several billion per second in air at room conditions. | 12.3 |
| Dalton's law of partial pressures | The total pressure of a mixture of ideal gases is the sum of the partial pressures, each being the pressure that gas would exert if it alone filled the container; each equals its mole fraction times the total. | 12.1 12.2 |
| degrees of freedom | The independent ways a molecule can move and store energy; counted as squared terms in its energy: $3$ for a monatomic molecule, $5$ for a rigid diatomic one, $6$ for a rigid non-linear one, plus $2$ for each active vibration. | 12.3 |
| Dulong–Petit law | The molar heat capacity of a solid element at ordinary temperatures is about $3R\approx25\ \text{J mol}^{-1}\text{K}^{-1}$, from $6$ squared energy terms per vibrating atom; it fails at low temperatures. | 12.3 |
| ideal gas | A model gas whose molecules have negligible volume and exert no forces on one another except in brief elastic collisions; it obeys $pV=nRT$ exactly. Real gases approach it at low pressure and high temperature. | 10.1 11.1 11.2 11.3 |
| kinetic interpretation of temperature | The result that the absolute temperature of an ideal gas measures the mean translational kinetic energy of its molecules: $\tfrac12m\overline{v^2}=\tfrac32k_BT$, the same for every gas at the same $T$. | 12.2 |
| kinetic theory of gases | The model that explains the properties of a gas from the motion of its molecules: many tiny molecules in random motion, colliding elastically, with Newton's laws applied to each. It gives $p=\tfrac13\rho\overline{v^2}$. | 11.1 11.2 12.2 |
| law of equipartition of energy | In thermal equilibrium at temperature $T$, each translational and rotational degree of freedom carries a mean energy $\tfrac12k_BT$ and each vibrational mode $k_BT$; so $U=\tfrac f2nRT$ and $C_v=\tfrac f2R$ for an ideal gas. | 12.3 14.2 |
| Maxwell speed distribution | The spread of molecular speeds in a gas in equilibrium, rising as $v^2$ and falling exponentially at high speeds; its peak is the most probable speed $\sqrt{2RT/M}$ (beyond the board syllabus). | 12.2 |
| mean free path | The average distance a gas molecule travels between successive collisions, $\lambda=\dfrac{1}{\sqrt2\,\pi d^2n_V}=\dfrac{k_BT}{\sqrt2\,\pi d^2p}$; about $60\ \text{nm}$ for air at STP. | 12.3 |
| mean square speed | The average of the squares of the molecular speeds, $\overline{v^2}=\dfrac{v_1^2+v_2^2+\dots+v_N^2}{N}$; it is larger than the square of the mean speed. | 12.2 |
| molar volume | The volume occupied by one mole of a gas, $V_m=\dfrac{RT}{p}$; for every ideal gas it is $22.4\ \text{L}$ at STP ($273\ \text{K}$, $1\ \text{atm}$). | 12.1 |
| partial pressure | The pressure one gas in a mixture would exert if it alone occupied the whole volume at the same temperature. | 12.1 12.2 |
| rms speed | The root-mean-square speed $v_\text{rms}=\sqrt{\overline{v^2}}=\sqrt{\dfrac{3RT}{M}}=\sqrt{\dfrac{3k_BT}{m}}$ of gas molecules; about $500\ \text{m/s}$ for air at room temperature. | 12.2 14.2 |
| vibrational mode | A way in which the atoms of a molecule oscillate relative to one another; when active it holds both kinetic and potential energy, $k_BT$ on average. Vibrations are usually frozen out at room temperature. | 12.3 |
Ch 13 · Oscillations
| Term | Meaning | Used in |
|---|---|---|
| acceleration amplitude | The greatest magnitude of acceleration $a_\text{max}=\omega^2A$ in SHM, reached at the extreme positions. | 13.2 |
| amplitude | The magnitude $A$ of the largest displacement from the mean position in an oscillation (half the total swing). | 1.3 13.1 13.2 13.3 |
| angular frequency | The constant $\omega$ in $x=A\cos(\omega t+\phi)$, in rad/s: $\omega=\dfrac{2\pi}{T}=2\pi\nu$; it equals the angular speed of the reference particle. | 13.1 13.2 13.3 14.1 |
| antiphase | Two oscillations of the same frequency are in antiphase when their phase difference is $\pi$: one is at its maximum when the other is at its minimum, as for $x$ and $a$ in SHM. | 13.1 13.2 14.1 14.3 |
| effective spring constant | The constant $k_\text{eff}$ of the single spring equivalent to a combination: $k_1+k_2$ in parallel, $\dfrac{k_1k_2}{k_1+k_2}$ in series. | 8.1 13.3 |
| hertz | The SI unit of frequency: $1\ \text{Hz}$ is one repetition (cycle) per second, $1\ \text{s}^{-1}$. | 1.1 3.4 13.1 13.3 |
| isochronism | The property of an oscillator whose period does not depend on its amplitude, as for any SHM and, approximately, for a pendulum at small amplitudes. | 13.3 |
| linear restoring force | A force $F=-kx$ proportional to the displacement from equilibrium and opposite to it; a body under such a force moves in SHM with $\omega=\sqrt{k/m}$. | 13.2 13.3 |
| mean position | The equilibrium position about which a body oscillates: placed there at rest, it feels no net force and stays put. | 13.1 13.2 13.3 14.1 |
| oscillatory motion | A periodic to-and-fro motion of a body about a fixed equilibrium (mean) position, kept going by a restoring force. | 13.1 |
| periodic motion | Motion that repeats itself exactly at regular intervals of time, e.g. uniform circular motion or a swinging pendulum. | 13.1 |
| phase constant | The value $\phi$ of the phase $\omega t+\phi$ of an SHM at $t=0$; it fixes where in its cycle the motion starts, $x(0)=A\cos\phi$. | 13.1 13.2 14.1 |
| phase difference | The constant difference $\delta=\phi_2-\phi_1$ between the phases of two oscillations of the same frequency; the one with the larger phase leads by a time $\delta/\omega$. | 13.1 13.2 14.1 14.3 |
| reference circle | A circle of radius $A$ round which a particle moves uniformly at angular speed $\omega$; its projection on a diameter performs the SHM $x=A\cos(\omega t+\phi)$. | 13.1 13.2 |
| seconds pendulum | A simple pendulum with a period of exactly $2\ \text{s}$ (one second per swing); on the Earth its length is about $0.993\ \text{m}$. | 13.3 |
| simple harmonic motion | Oscillation along a line in which the displacement varies with time as a single cosine, $x=A\cos(\omega t+\phi)$; equivalently, motion under a restoring force $F=-kx$. | 13.1 13.2 13.3 14.1 |
| simple pendulum | A point mass on a light inextensible string of length $l$ swinging in a vertical plane; for small swings $T=2\pi\sqrt{l/g}$. | 1.3 5.2 13.3 |
| small-angle approximation | Replacing $\sin\theta$ by $\theta$ (in radians) for small angles; it is better than $0.5\%$ up to about $10^\circ$ and makes the pendulum's motion SHM. | |
| springs in parallel | Springs side by side with the same extension; their forces add, so $k_\text{p}=k_1+k_2$. | |
| springs in series | Springs joined end to end; each carries the same tension and the extensions add, so $\dfrac1{k_\text{s}}=\dfrac1{k_1}+\dfrac1{k_2}$. | 13.3 |
| spring–block oscillator | A block attached to a light spring, oscillating in SHM under the spring force $-kx$ with period $T=2\pi\sqrt{m/k}$. | 13.3 14.4 |
| time period | The smallest time $T$ after which a periodic motion repeats itself; the frequency is $\nu=\dfrac1T$. | 13.1 |
| velocity amplitude | The greatest speed $v_\text{max}=\omega A$ of a particle in SHM, reached as it passes through the mean position. | 13.2 |
Ch 14 · Waves
| Term | Meaning | Used in |
|---|---|---|
| adiabatic bulk modulus | The bulk modulus of a gas compressed without heat exchange, $B=\gamma p$; compressed slowly at constant temperature it is the isothermal modulus $B=p$. | 14.2 |
| antinode | A point of a standing wave where the amplitude of oscillation is greatest; it lies midway between two nodes, $\dfrac\lambda4$ from each. | 14.3 |
| beat frequency | The number of loudness maxima per second in beats, $\nu_\text{beat}=|\nu_1-\nu_2|$. | 14.4 |
| beat period | The time between two successive loudness maxima in beats, $T_\text{beat}=\dfrac{1}{|\nu_1-\nu_2|}$. | 14.4 |
| beats | The periodic rise and fall in loudness heard when two sounds of slightly different frequencies superpose; the waves drift into and out of step. | 14.4 |
| Doppler effect | The change in observed frequency when the source or observer of a wave moves (beyond the NCERT syllabus): $\nu'=\nu\dfrac{v+v_o}{v-v_s}$ for motion towards each other. | 14.4 |
| fundamental | The normal mode of lowest frequency (the first harmonic): $\dfrac{v}{2L}$ for a string fixed at both ends or an open pipe, $\dfrac{v}{4L}$ for a pipe closed at one end. | 14.3 14.4 |
| harmonics | Normal modes whose frequencies are whole-number multiples of the fundamental: the $n$th harmonic has frequency $n\nu_1$. A closed pipe has only the odd harmonics. | 14.3 14.4 |
| interference | The change in resultant amplitude when waves overlap: constructive where they arrive in phase (amplitudes add), destructive where they arrive in antiphase (they cancel). | 14.3 |
| Laplace correction | Laplace's recognition that the compressions of a sound wave are adiabatic, so the bulk modulus is $\gamma p$ and $v=\sqrt{\gamma p/\rho}=\sqrt{\gamma RT/M}$. | 14.2 |
| linear mass density | Mass per unit length $\mu=\dfrac mL$ of a string or wire (kg/m); for a wire of density $\rho$ and cross-section $A$, $\mu=\rho A$. | 14.2 14.3 |
| longitudinal wave | A wave in which the elements of the medium oscillate along the direction of travel, forming compressions and rarefactions, e.g. sound in air. | 14.1 14.2 14.3 |
| mechanical wave | A disturbance that travels through a material medium because of the elastic forces between its parts; each element only oscillates about its mean position, while energy and momentum are carried along. | 14.1 14.2 |
| Newton's formula (speed of sound) | Newton's estimate $v=\sqrt{p/\rho}$ for the speed of sound in a gas, which assumes isothermal compressions; it is too low by the factor $\sqrt\gamma$ (about $280\ \text{m/s}$ for air at $0\ ^\circ\text{C}$). | 14.2 |
| node | A point of a standing wave that is always at rest; neighbouring nodes are $\dfrac\lambda2$ apart. | 14.3 14.4 |
| normal modes | The natural standing-wave patterns of a vibrating system (string, air column), each with its own frequency, in which every part moves in SHM at that frequency. | 14.3 |
| overtones | The normal modes above the fundamental, numbered in order: for a string the first overtone is the 2nd harmonic; for a closed pipe it is the 3rd harmonic. | 14.3 |
| principle of superposition | When waves overlap, the resultant displacement is the algebraic sum of the displacements each wave would cause alone, and each wave travels on unaltered. | 7.1 14.3 14.4 |
| progressive wave | A wave whose pattern moves through the medium at a steady speed, e.g. $y=a\sin(kx-\omega t+\phi)$ travelling towards $+x$. | 14.1 14.3 |
| rarefaction | A region of a longitudinal wave where the medium is stretched out (lower density and pressure than normal); it alternates with compressions, half a wavelength apart. | 14.1 14.2 |
| reflection of waves | The return of a wave from a boundary with unchanged frequency and speed; at a rigid boundary the phase changes by $\pi$ (a pulse returns inverted), at an open boundary there is no phase change. | 14.3 |
| seismic wave | A wave through the Earth from an earthquake: the faster P-wave is longitudinal, the slower S-wave is transverse and cannot cross the liquid outer core. | 14.1 |
| sonar | Locating objects under water by timing the echoes of sound pulses: distance $=\dfrac{v\,t}{2}$ for an echo returning after a time $t$. | 14.2 |
| speed of sound | The speed of longitudinal waves in a medium, $v=\sqrt{B/\rho}$ in a fluid ($\sqrt{Y/\rho}$ along a thin rod); about $343\ \text{m/s}$ in air at $20\ ^\circ\text{C}$. | 1.3 2.3 6.3 9.2 |
| standing wave | A non-travelling pattern, e.g. $y=2a\sin kx\cos\omega t$, formed by two identical waves moving in opposite directions; each point oscillates with an amplitude fixed by its position. | 14.3 14.4 |
| timbre | The quality of a musical sound that depends on the mixture of harmonics present, which is why different instruments playing the same note sound different. | 14.3 |
| transverse wave | A wave in which the elements of the medium oscillate perpendicular to the direction of travel, e.g. a wave on a stretched string or an S-wave in rock. | 14.1 14.2 |
| tuning fork | A two-pronged steel fork that vibrates at one steady, nearly pure frequency; loading a prong with wax lowers the frequency and filing the prongs raises it. | 14.3 14.4 |
| ultrasound | Sound of frequency above the range of human hearing (above about $20\ \text{kHz}$); its short wavelength lets it image small structures, as in medical scanners and bat echolocation. | 14.1 14.2 14.4 |
| wave number | The angular wave number $k=\dfrac{2\pi}{\lambda}$ (rad/m): the phase change per metre along a wave. | 14.1 14.3 |
| wave pulse | A single short disturbance (one hump or one squeeze) travelling through a medium, as opposed to a periodic wave that repeats at regular intervals. | |
| wave speed | The speed $v=\dfrac{\omega}{k}=\nu\lambda$ at which the pattern of a wave moves through the medium; it is set by the medium, not by the source. | 1.3 14.1 14.2 14.3 |
| wavelength | The smallest distance $\lambda$ between two points of a wave that are always in the same phase, e.g. crest to crest or compression to compression. | 1.3 10.3 14.1 14.2 |