Mass in motion
Which is harder to stop: a bowling ball rolling slowly or a ping-pong ball rolling at the same speed? The bowling ball, because it has more momentum. Momentum is "mass in motion."
momentum = mass × velocity
p = m × v
Units: kilogram-metres per second (kg·m/s).
Momentum has a direction (the same as velocity), so it’s a vector.
| Object | Mass | Speed | Momentum |
|---|---|---|---|
| Soccer ball | 0.43 kg | 25 m/s | 10.75 kg·m/s |
| Hockey player | 90 kg | 8 m/s | 720 kg·m/s |
| Car | 1500 kg | 20 m/s | 30 000 kg·m/s |
| Freight train | 5 000 000 kg | 10 m/s | 50 000 000 kg·m/s |
A slow train has enormous momentum because of its huge mass. That’s why trains need more than a kilometre to stop.
Changing momentum: impulse
To change an object’s momentum, you need a force acting for some time. This is called impulse.
impulse = force × time = change in momentum
The same change in momentum can come from:
- a big force for a short time (a hard, quick hit), or
- a small force for a long time (a gentle, slow stop).
Safety: spreading out the time
Many safety features work by increasing the time of a collision, which reduces the force.
| Safety feature | How it works |
|---|---|
| Airbags | Cushion the head, increasing stopping time |
| Seat belts | Stretch slightly to slow you more gradually |
| Car crumple zones | Crush slowly to lengthen the crash time |
| Bike and hockey helmets | Foam squishes to slow the head gradually |
| Gym mats and trampolines | Increase landing time |
| Bending your knees when you land | Spreads the stop over more time |
| Catching a ball by pulling your hands back | Increases catching time, so it stings less |
Sports: increasing the time
Athletes "follow through" when hitting a ball. Keeping the bat, racket or club in contact longer increases the impulse and sends the ball faster.
Conservation of momentum
In a closed system (with no outside forces), the total momentum before a collision equals the total momentum after.
total momentum before = total momentum after
This is the conservation of momentum, and it comes from Newton’s third law.
Example: bumper cars
A 100 kg bumper car moving at 3 m/s hits a stationary 100 kg bumper car. They lock together.
- Momentum before = 100 × 3 + 100 × 0 = 300 kg·m/s
- After, the combined mass is 200 kg: 200 × v = 300
- v = 1.5 m/s
Example: recoil
When a skateboarder throws a heavy ball forward, the skateboarder rolls backward. Before the throw, total momentum was zero. After, the ball’s forward momentum is balanced by the skateboarder’s backward momentum.
Rockets work the same way: hot gases blast backward, and the rocket moves forward.
Types of collisions
| Type | What happens | Kinetic energy | Example |
|---|---|---|---|
| Elastic collision | Objects bounce off each other | Conserved | Pool balls (nearly), atoms in a gas |
| Inelastic collision | Objects bounce but lose some energy | Partly lost as heat, sound, deformation | A basketball bouncing |
| Perfectly inelastic | Objects stick together | Most lost | Two train cars coupling, a football tackle |
Momentum is conserved in all types. Kinetic energy is conserved only in elastic collisions.
Newton’s cradle
In a Newton’s cradle, one ball swings in and one ball swings out the other side at nearly the same speed. Both momentum and kinetic energy are (almost) conserved.
Common mistakes
- Thinking a heavy object always has more momentum. A fast light object can have more momentum than a slow heavy one.
- Thinking momentum and kinetic energy are the same. Momentum is always conserved in collisions; kinetic energy often isn’t.
- Forgetting direction. Momenta in opposite directions subtract.
Try it yourself
- Roll a marble into a stationary marble. Then roll a marble into a line of three. What do you notice?
- Drop an egg onto a hard floor and onto a thick pillow (in a bag!). Explain the difference using impulse.
- A 60 kg skater moving at 2 m/s collides with and holds onto a 40 kg skater at rest. What is their combined speed?
(Answer to 3: 120 ÷ 100 = 1.2 m/s)
Quick recap
- Momentum = mass × velocity.
- Impulse (force × time) changes momentum.
- Increasing collision time reduces force, which is the idea behind many safety features.
- Momentum is conserved in collisions.
- Elastic collisions also conserve kinetic energy; inelastic ones don’t.