What is momentum?
Momentum measures how hard it is to stop a moving object. It depends on both the object's mass and its velocity. Because velocity has direction, momentum is a vector: it has size and direction. The SI unit is the kilogram metre per second (kg·m/s).
Key idea
momentum = mass × velocity, so p = m v. Unit: kg·m/s. A resultant force equals the rate of change of momentum: F = (mv − mu)/t.
Conservation of momentum
When objects interact (for example in a collision or an explosion) and no external resultant force acts, the total momentum before an event equals the total momentum after it. Add momenta as vectors: choose a positive direction and treat motion the opposite way as negative.
Worked example
A 2.0 kg trolley moving at 3.0 m/s collides with a stationary 1.0 kg trolley and they stick together. Find their common velocity v.
Total momentum before = (2.0 × 3.0) + (1.0 × 0) = 6.0 kg·m/s.
Total momentum after = (2.0 + 1.0) × v = 3.0 v.
So 3.0 v = 6.0, giving v = 2.0 m/s in the original direction.
Remember
- Momentum is a vector — include direction (+ or −).
- Force = change in momentum ÷ time.
- Total momentum is conserved only when no external resultant force acts.