Conservation of Momentum
Overview
In a closed system (no net external force), the total momentum before an interaction equals the total momentum after: Σp_before = Σp_after. This applies to all collisions and explosions. Choose a positive direction first, then assign signs to velocities accordingly. Works in all directions independently.
The Law of Conservation of Momentum
In a closed system (no external forces), the total momentum before an event equals the total momentum after: Σp_before = Σp_after. This follows directly from Newton's 3rd Law — during a collision, the force A exerts on B equals and opposite the force B exerts on A, so the total impulse is zero and total momentum doesn't change. 'Closed system' means the net external force is zero.
Applying conservation: step by step
Step 1: Define a positive direction. Step 2: Write momentum for each object before the collision: p₁ = m₁v₁, p₂ = m₂v₂ (use signs for direction). Step 3: Write total momentum after, with unknowns. Step 4: Set before = after and solve. For objects that stick together (perfectly inelastic): m₁v₁ + m₂v₂ = (m₁ + m₂)v_f.
- ⚠Forgetting to use vector signs for velocity — a leftward velocity should be negative
- ⚠Applying conservation of kinetic energy when only momentum conservation was stated
- ⚠Using conservation of momentum when there IS a significant external force (e.g., an explosion on a braking car)