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Class XI · Chapter 04

Laws of Motion

Three deceptively short rules from Newton that explain everything from why a bus jerks you forward when it brakes to why rockets work in the vacuum of space.

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1Aristotle's Fallacy and the Idea of Inertia

Aristotle believed a force was needed continuously just to keep something moving — a natural-enough conclusion from everyday experience, since a pushed cart does stop once you let go. Galileo (and later Newton) recognised the flaw: the cart stops because of friction, an opposing force, not because motion itself requires a sustaining push. Remove friction entirely, and an object in motion would simply keep moving forever — this tendency to resist changes in motion is inertia, and it's the real foundation classical mechanics is built on.

2Newton's First Law of Motion

Newton's First Law An object remains at rest, or continues moving at constant velocity in a straight line, unless acted upon by a net external force.

This law does two things at once: it defines force (as whatever is needed to change an object's state of motion), and it defines what an inertial frame of reference is — one in which this law actually holds true.

3Newton's Second Law of Motion

The first law says a net force is needed to change motion; the second law quantifies exactly how.

Newton's Second Law
F = dp/dt, or F = ma (for constant mass)
p = mv is momentum. Force is the rate of change of momentum — a more general statement than F=ma, since it still applies even when mass itself is changing (like a rocket burning fuel).
Impulse
J = FΔt = Δp
For a very large force acting over a very short time (a bat hitting a ball, a car crash), impulse — the product of force and time — is often more useful than force alone, since it directly equals the resulting change in momentum.

4Newton's Third Law of Motion

Newton's Third Law For every action, there is an equal and opposite reaction — forces always occur in pairs.
Third Law
FAB = − FBA
Common Slip Action-reaction pairs act on two different bodies — they never cancel each other out for either object individually. A book resting on a table doesn't stay still because the table's push "cancels" gravity via Newton's third law; it stays still because those two forces (gravity on the book, and the normal force on the book) happen to balance, which is Newton's first law, not the third.

5Conservation of Momentum

Combine the second and third laws, and a powerful result falls out directly: if no net external force acts on a system, its total momentum stays exactly constant over time — regardless of whatever internal forces (collisions, explosions, interactions) happen within it.

Conservation of Momentum
ptotal = constant, when Fexternal = 0
This single principle underlies collisions, explosions, and rocket propulsion — a rocket accelerates forward precisely because it throws exhaust gas backward, conserving total momentum of the rocket-plus-exhaust system, even in the vacuum of space where there's nothing to "push against."

6Equilibrium of a Particle

Condition for Equilibrium
ΣF = 0
A particle is in equilibrium exactly when the vector sum of every force acting on it is zero — it need not be at rest (constant velocity in a straight line satisfies this too, by the first law).

7Common Forces in Mechanics

  • Weight: gravitational force on an object, W = mg, always directed downward.
  • Normal force (N): the perpendicular contact force a surface exerts, preventing objects from passing through it.
  • Tension (T): the pulling force transmitted through a string or rope, directed along its length.
  • Friction (f): the force resisting relative sliding between two surfaces in contact — covered in detail next.

8Friction

Static Friction (Before Motion Begins)
fs ≤ μs N
Static friction is self-adjusting — it grows to match whatever applied force is trying to cause sliding, up to a maximum value μsN, beyond which the object finally starts to move.
Kinetic Friction (Once Sliding)
fk = μk N
Roughly constant once motion begins, and μk is generally somewhat smaller than μs — which is exactly why it takes a noticeably harder push to start something sliding than to keep it sliding.

9Circular Motion Dynamics

Chapter 3 established that circular motion requires centripetal acceleration; this section asks what actually provides that force in real situations — tension in a string, gravity for orbiting satellites, friction for a car on a flat curve, or the normal force on a banked track.

Required Centripetal Force
Fc = mv² / r
Ideal Banking Angle (No Friction Needed)
tan θ = v² / (rg)
Banking a curved road at this precise angle lets the horizontal component of the normal force alone supply the needed centripetal force — no reliance on friction at all, which is exactly why banked racetrack curves allow much higher safe speeds than flat ones.

Formula Summary

Second Law
F = dp/dt = ma
Impulse
J = FΔt = Δp
Third Law
F_AB = −F_BA
Equilibrium
ΣF = 0
Static Friction
f_s ≤ μ_s N
Kinetic Friction
f_k = μ_k N
Centripetal Force
F_c = mv²/r
Banking Angle
tanθ = v²/rg

Solved Examples

Example 1 · Newton's Second Law

A force of 10 N acts on a 2 kg mass initially at rest. Find its acceleration and its velocity after 5 s.

Solution: a = F/m = 10/2 = 5 m/s².

v = u + at = 0 + 5×5 = 25 m/s.

Example 2 · Static Friction

A 5 kg block rests on a horizontal surface with μs = 0.4. Find the maximum horizontal force that can be applied without the block moving. (g = 10 m/s²)

Solution: fmax = μsN = μsmg = 0.4 × 5 × 10 = 20 N.

Any applied force up to 20 N is exactly matched by static friction, keeping the block at rest; beyond 20 N, it starts to slide.

Quick Check

1. Newton's third law action-reaction pairs:
Act on the same body and cancel out
✓ Act on two different bodies (correct)
Only apply to contact forces
Only apply in a vacuum
2. At the ideal banking angle for a curved road, the centripetal force is provided by:
Friction alone
Weight alone
✓ The horizontal component of the normal force (correct)
Tension in the road surface
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Motion in a Plane

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Work, Energy and Power

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