A rolling bowling ball is hard to stop, and so is a fast baseball. Momentum measures this "hard to stop": it combines mass with velocity. The third law explains why it is conserved.
Key idea
Momentum $p = m\,v$, in kg·m/s. In a collision, the total momentum of the objects is the same before and after (as long as outside forces are small).
Why it works
When two carts collide, each pushes the other with the same force for the same short time. One cart gains exactly the momentum the other loses, so the total cannot change. Momentum has a direction too: on a line, momentum to the left is negative.
Worked example: Heavy and slow or light and fast?
Which has more momentum: a 1,500 kg car at 2 m/s or a 0.15 kg baseball at 40 m/s?
- Car: $p = 1{,}500 \times 2 = 3{,}000$ kg·m/s.
- Baseball: $p = 0.15 \times 40 = 6$ kg·m/s.
- The slow car has 500 times more.
Answer: The car
Worked example: Stick together
A 2 kg cart moving at 3 m/s hits a 1 kg cart at rest, and they stick. How fast do they move together?
- Momentum before: $2 \times 3 + 1 \times 0 = 6$ kg·m/s.
- After, the carts move together with mass $2 + 1 = 3$ kg and the same total momentum.
- $v = \dfrac{6}{3} = 2$ m/s.
Answer: 2 m/s
Common mistake
Thinking a heavy, slow object always has more momentum than a light, fast one. Momentum is mass times velocity, so a big enough speed can win: a 60 kg runner at 8 m/s ($480$) has more momentum than a 200 kg cart at 2 m/s ($400$). Check: multiply both before you compare.
Crash gliders on an air track in the Science Lab: Momentum and Collisions.