Chapter 4 · Introduction

Chapter 4 — Laws of Motion

Chapters 2 and 3 described how things move. This chapter explains why: forces change motion, momentum is passed from body to body, and friction and circular paths follow from three short laws.

A magician whips a tablecloth from under a full dinner service and the plates hardly move. A bus brakes suddenly and the standing passengers lurch forward, although nobody pushed them. A cricketer catching a fast ball draws her hands back as the ball arrives. A rocket in empty space, with nothing to "push against", still speeds up. A car taking a bend too fast on a wet road slides off the outside of the curve. Each of these is the same physics in a different costume, and by the end of this chapter you will be able to put numbers on every one of them.

Isaac Newton gathered the answer into three laws. The first law says that a body left to itself keeps its velocity — motion needs no cause, only changes of motion do. The second law says how a net force changes a body's momentum, $\mathbf{F}=\dfrac{d\mathbf{p}}{dt}$, which for a body of fixed mass is $\mathbf{F}=m\mathbf{a}$. The third law says forces always come in equal and opposite pairs, and from it follows one of the great conservation laws of physics: the total momentum of an isolated system never changes. With these laws, plus a few everyday forces — weight, the normal force, tension and friction — you will solve problems on blocks and slopes, pulleys and connected bodies, lifts, recoiling guns and cars on banked roads.

Inertia→First law→Momentum→$\mathbf{F}=\dfrac{d\mathbf{p}}{dt}$→Impulse→Third law→Momentum conservation→Equilibrium & friction→Circular motion
🎯 By the end of this chapter you can…
  • explain why Aristotle's idea that motion needs a force is wrong, and state and use the law of inertia (Newton's first law);
  • define linear momentum, state Newton's second law as $\mathbf{F}=\dfrac{d\mathbf{p}}{dt}$ and use $\mathbf{F}=m\mathbf{a}$ in vector and component form;
  • use impulse $=\mathbf{F}\,\Delta t=\Delta\mathbf{p}$ and the area under a force–time graph to explain catching, airbags and impulsive forces;
  • identify action–reaction pairs correctly and use the conservation of linear momentum for recoil, explosions and bodies that stick together;
  • draw free-body diagrams, apply the conditions for equilibrium of a particle, and work with weight, normal force, tension and static, kinetic and rolling friction;
  • find the speed limits for a car on a level or banked curve, and solve problems on connected bodies, pulleys and lifts;
  • solve Board, JEE Main, JEE Advanced and NEET-style problems on the laws of motion.
Teaser — The Coin, the Card and the Glass

A coin rests on a card laid over a glass, with its centre $4.0\ \text{cm}$ from the card's back edge. You pull the card sideways with a steady acceleration. Predict first: does a gentle pull or a sharp flick drop the coin into the glass? Then choose the acceleration of the pull and press Play (the motion is shown in slow motion). Coin–card friction: $\mu_s=0.30$, $\mu_k=0.25$; the glass mouth has radius $3.5\ \text{cm}$.

2 m/s²
greatest acceleration friction can give the coin—
coin's acceleration—
coin's shift while the card slides out—

Sections in this chapter

4.1

Inertia, Momentum and Newton's First and Second Laws

Why motion needs no cause, the law of inertia, linear momentum, $\mathbf{F}=m\mathbf{a}$ and impulse.

$\mathbf{F}=\dfrac{d\mathbf{p}}{dt}=m\mathbf{a}$
Open section →4.2

Newton's Third Law and Conservation of Momentum

Action–reaction pairs, why they never cancel, and momentum conservation in recoil, explosions and collisions.

$m_1\mathbf{v}_1+m_2\mathbf{v}_2=\text{constant}$
Open section →4.3

Equilibrium of a Particle, Common Forces and Friction

Free-body diagrams, balanced forces, weight, normal force, tension, and static, kinetic and rolling friction.

$f_s\le\mu_sN,\quad f_k=\mu_kN$
Open section →4.4

Circular Motion and Solving Problems in Mechanics

The force needed to turn, cars on level and banked roads, connected bodies, pulleys and lifts.

$v_0=\sqrt{rg\tan\theta}$
Open section →
✅ Before you start
You will use acceleration and the kinematic equations (Section 2.2, Section 2.3) all through this chapter, and the area under a graph (Section 2.2) for impulse. Forces are vectors, so you need vector addition and, above all, resolving a vector into components along chosen axes (Section 3.1, Section 3.2). Section 4.4 builds on centripetal acceleration $a_c=v^2/r$ (Section 3.4). From Class 10 Science, recall the idea of force, mass and weight, and that the newton is the unit of force; from mathematics, the values of $\sin$, $\cos$ and $\tan$ and solving simultaneous linear equations.
← 3.4 Uniform Circular Motion4.1 Inertia, Momentum and Newton's First and Second Laws →