Newton's Laws and Equilibrium
~9 min read
- Three laws: 1st: inertia. 2nd: F = ma. 3rd: action = reaction.
- Equilibrium: Net force = 0 and net torque = 0. Stable, unstable, neutral types.
- Validity: Newton's laws fail at speeds close to that of light (relativity) and at atomic scales (quantum mechanics).
Newton's three laws of motion are the spine of classical mechanics and a near-certain CDS/OTA question every year. They define force, link it with mass and acceleration, and explain why action always produces reaction.
Newton's Three Laws
| Law | Statement | Everyday example |
|---|---|---|
| First (Inertia) | A body at rest stays at rest; in motion stays in uniform motion — unless acted on by an external force | Passengers lurch forward when a bus brakes |
| Second | F = ma. Rate of change of momentum equals applied force | Heavier truck needs more force to accelerate |
| Third | Every action has an equal and opposite reaction | Rocket propulsion, recoil of gun, swimming |
Units: Force in newton (N) = kg·m/s². Momentum p = mv in kg·m/s. Mass measures inertia.
Equilibrium of Forces
- Translational equilibrium: ΣF = 0 — net force zero.
- Rotational equilibrium: Στ = 0 — net torque zero.
- Stable: body returns to original position after small displacement (centre of gravity low).
- Unstable: body moves further away (centre of gravity high, narrow base).
- Neutral: body stays wherever displaced (rolling ball).
Momentum and Impulse
- Momentum p = mv — vector, kg·m/s.
- Impulse J = F·t = Δp — change in momentum.
- Seat belts and airbags increase Δt and reduce force on the body (same Δp).
- Conservation of momentum: In an isolated system, total momentum is conserved — basis of rocket propulsion and recoil.
When Newton's Laws Fail
- At velocities close to light (Einstein's special relativity takes over).
- At atomic/sub-atomic scales (quantum mechanics).
- In strong gravitational fields (general relativity).
- For everyday speeds and ordinary objects, Newton's laws are accurate to many decimal places.
CDS/OTA PYQ Examples
Q: Newton's laws of motion do not hold good for objects:
(a) at rest (b) moving slowly (c) moving with high velocity (d) moving with velocity comparable to velocity of light
Answer: (d) — at near-light speeds, relativity is required. [CDS-II 2015]
Q: A rocket moves forward because of:
(a) Newton's first law (b) Newton's second law (c) Newton's third law (d) Archimedes' principle
Answer: (c) Third law — hot gases ejected backward push the rocket forward.
Q: The SI unit of force is:
(a) Joule (b) Newton (c) Watt (d) Pascal
Answer: (b) Newton = kg·m/s².
Q: Inertia of a body depends on its:
(a) Weight (b) Mass (c) Velocity (d) Volume
Answer: (b) Mass — more mass, more inertia.
Q: When a man jumps from a boat to shore, the boat moves backward. This illustrates:
(a) Newton's first law (b) Newton's second law (c) Newton's third law (d) Law of gravitation
Answer: (c) Third law / conservation of momentum.
Drill Newton's Laws and Equilibrium for CDS/OTA
CDS/OTA-pattern items on Newton's Laws and Equilibrium with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why do passengers fall forward when a bus stops suddenly?
Inertia of motion — bodies continue moving while the bus decelerates, so passengers lurch forward until restrained by a seat belt or the seat ahead.
What is the difference between mass and weight?
Mass is the amount of matter (kg, scalar, constant). Weight is the gravitational force on that mass (W = mg, in newton, varies with location).
Why does a gun recoil?
Conservation of momentum. Bullet leaves with forward momentum mv; gun must move backward with equal and opposite momentum MV, so V = mv/M.
Is Newton's first law a special case of the second?
Yes — if F = 0 in F = ma, acceleration is zero, so velocity stays constant. The first law historically defines the concept of force and inertia.