Momentum and Conservation Laws
~9 min read
- Linear momentum: p = mv. Vector. SI unit: kg·m/s.
- Conservation: Total momentum of an isolated system is constant. Applies to collisions, recoil, explosions.
- Collisions: Elastic — both p and KE conserved. Inelastic — p conserved, KE not. Perfectly inelastic — bodies stick.
Momentum is mass in motion. Its conservation in isolated systems explains gun recoil, rocket flight, and collision outcomes — all favourites of CDS/OTA Science.
Momentum and Impulse
- Momentum p = mv — vector quantity.
- Newton's second law: F = dp/dt.
- Impulse J = F·Δt = Δp — change in momentum produced by a force acting for time Δt.
- Long contact time → smaller force for the same Δp. This is why seat belts, airbags, packaging foam and crumple zones save lives.
Conservation of Momentum
For an isolated system (no external force), total momentum before = total momentum after.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- Recoil of gun: 0 = MV + mv → V = -mv/M (gun moves backward).
- Rocket propulsion: hot gases ejected backward give rocket forward momentum.
- Explosion of a stationary shell: fragments' momenta vector-sum to zero.
Types of Collisions
| Type | Momentum | Kinetic energy | Example |
|---|---|---|---|
| Elastic | Conserved | Conserved | Gas molecules, billiard balls (approx) |
| Inelastic | Conserved | Not conserved | Car crash with deformation |
| Perfectly inelastic | Conserved | Maximum loss | Bullet embedded in wooden block |
CDS/OTA PYQ Examples
Q: The principle behind rocket propulsion is:
(a) Newton's first law (b) Conservation of energy (c) Conservation of momentum (d) Archimedes' principle
Answer: (c) Conservation of momentum.
Q: SI unit of momentum is:
(a) kg·m/s (b) N·m (c) kg·m/s² (d) J·s
Answer: (a) kg·m/s (also N·s).
Q: In an elastic collision:
(a) Only momentum is conserved (b) Only KE is conserved (c) Both momentum and KE conserved (d) Neither
Answer: (c) Both.
Q: A bullet of mass 20 g fired with velocity 400 m/s from a gun of mass 4 kg. Recoil velocity of gun is:
(a) 1 m/s (b) 2 m/s (c) 4 m/s (d) 8 m/s
Answer: (b) 2 m/s. MV = mv → V = (0.02 × 400)/4 = 2 m/s.
Drill Momentum and Conservation Laws for CDS/OTA
CDS/OTA-pattern items on Momentum and Conservation Laws with answer keys and explanations.
Start Free Mock TestFrequently Asked Questions
Why do seat belts save lives?
They extend the time over which a passenger's momentum changes during a crash, reducing the force on the body (F = Δp/Δt).
Why is a karate chop more effective than a slow push?
Short contact time means high force for the same impulse — concentrating impact on a small area.
Can momentum of a single object change while total system momentum is conserved?
Yes — that is exactly what conservation says. Individual momenta change but their vector sum stays constant.