Momentum & Its Conservation

• Linear momentum p = mv (kg·m/s); vector in direction of velocity.
• Impulse = change in momentum = F × t (when F constant).
• Law of conservation of momentum — total momentum unchanged if no external force.
• Collisions, recoil of gun, rocket motion (introductory).

1. Momentum — p = mv; depends on mass and velocity.
2. Second law form — F = Δp/Δt (rate of change of momentum).
3. Conservation — m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (isolated system).
4. Elastic vs inelastic — Class 9 focus: total momentum conserved in both (kinetic energy may not be).
5. Diagram (text) — two ice skaters push apart: equal and opposite Δp.
6. NCERT Ch. 9 — gun recoil; collision of two similar trolleys on frictionless track.
7. Real world — cricketer pulls hands back while catching (increases Δt, reduces F).
8. Units — kg·m/s (same as N·s for impulse).

Collision: 2 kg cart at 3 m/s hits 2 kg cart at rest; they stick together. Find final velocity.

Given: m₁ = m₂ = 2 kg, u₁ = 3 m/s, u₂ = 0
Step 1 — Conservation: m₁u₁ + m₂u₂ = (m₁ + m₂)v
Step 2 — 2 × 3 + 0 = 4v → v = 6/4 = 1.5 m/s
Step 3 — Direction same as initial moving cart.
Step 4 — Momentum before = 6 kg·m/s; after = 4 × 1.5 = 6 kg·m/s ✓

• Using momentum conservation when external force acts (friction on track).
• Misconception: heavier object always has more momentum (need velocity too).
• Adding momenta as scalars when directions differ (vector addition needed).
• Confusing impulse with force.
• Forgetting that in recoil, total momentum before = 0 (gun + bullet system).

• Define momentum and state its SI unit.
• Why does a gun recoil when fired?
• A 0.05 kg ball at 20 m/s is caught. Find change in momentum.
• When is momentum of a system conserved?

Open the Practice tab for graded questions on Momentum & Its Conservation.