Laws of Motion – Class 11 Physics Chapter 4 Notes & NCERT PDF

Introduction

Chapter 3 described motion — position, velocity, acceleration — without asking why bodies move as they do. This chapter answers that question. The book begins with an everyday puzzle: a football needs a kick to move, a stone needs a push to rise, yet a moving body eventually stops. What is the role of force? Newton's three laws give the answer, and with them we can solve almost every problem of everyday mechanics.

Key Concepts

4.2 Aristotle's Fallacy

Aristotle held that an external force is required to keep a body in motion. This seems true because in daily life friction and air resistance always oppose motion — we must keep pushing a cart to keep it moving. The error is that the force we apply is needed only to cancel the opposing forces, not to maintain motion.

4.3 The Law of Inertia — Galileo

Galileo studied balls on double inclined planes. A ball rolling down one smooth plane climbs almost the same height on the opposite plane, whatever its slope. If the second plane is made horizontal, the ball should roll on forever. His conclusion:

The state of rest and the state of uniform linear motion (motion with constant velocity) are equivalent. In both cases no net force is acting.

The resistance of a body to a change in its state of motion is called inertia.

4.4 Newton's First Law

Every body continues to be in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise.

If the net external force is zero, acceleration is zero. The book's examples: a passenger jerked backward when a bus starts suddenly, and thrown forward when it stops; an astronaut who slips out of a spaceship accelerating at 100 m s⁻² has zero acceleration the instant he is outside (no force acts on him in deep space) — Example 4.1.

4.5 Newton's Second Law

Newton defined momentum p = m v (a vector, SI unit kg m s⁻¹).

The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts.

F = k dp/dt; choosing the SI unit of force makes k = 1, so F = dp/dt = m a (for constant mass). The newton: 1 N = 1 kg m s⁻². Key points: F = 0 gives a = 0 (consistent with the first law); the law is a vector law and applies to each component; it is local — a at a point depends on F at that point at that instant.

Impulse: when a large force acts for a very short time (a bat hitting a ball), we use

Impulse = Force × time duration = change in momentum.

4.6 Newton's Third Law

To every action, there is always an equal and opposite reaction.

Forces always occur in pairs; action and reaction act on different bodies and act simultaneously — neither is the "cause" of the other. So they never cancel each other in the equation of motion of a single body.

4.7 Conservation of Momentum

From the second and third laws: the total momentum of an isolated system of interacting particles is conserved. A bullet fired from a gun: initial momentum zero, so p(bullet) = −p(gun) — the gun recoils. In a collision, the impulses on the two bodies are equal and opposite, so total momentum before = total momentum after.

4.8 Equilibrium of a Particle

A particle is in equilibrium if the net external force is zero. For three concurrent forces, F₁ + F₂ + F₃ = 0 — they can be represented by the sides of a triangle taken in order. In component form, ΣFx = 0, ΣFy = 0, ΣFz = 0.

4.9 Common Forces in Mechanics

- Static friction fs adjusts itself up to a limit: fs ≤ μs N.

- Kinetic friction fk = μk N, nearly independent of contact area and speed; generally μk < μs.

- Rolling friction is much smaller, which is why the wheel was a great invention; lubricants and ball-bearings reduce friction further.

- Friction is not always a nuisance — walking, braking and holding objects all depend on it.

4.10 Circular Motion

A body moving in a circle of radius R with speed v needs a centripetal force m v²/R directed towards the centre.

4.11 Solving Problems in Mechanics

The book's method: draw a diagram; choose one body of the system; draw its free-body diagram showing all forces on it by other bodies; include forces from interacting bodies using the third law; apply the second law along chosen axes; repeat for other bodies.

Worked Examples

Formula / Key-Facts Sheet

Exam Focus

Common CBSE questions from the exercises: net force on bodies in given states of motion (Ex 4.1-type), retarding force from speed data (Exercise 4.5: 50 N on 20 kg gives a = −2.5 m s⁻²), lift problems (apparent weight = m(g ± a)), recoil and rocket problems, pulley systems with two masses, and conceptual "action–reaction" questions.

Key Terms

Common Mistakes