Momentum

Which one is harder to stop?

A cricket ball and a tennis ball come at you at the same speed: the cricket ball is harder to stop. A cricket ball tossed gently and one hit hard: the fast one is harder to stop. Both the mass and the velocity matter.

Momentum

Momentum $p$ is mass times velocity, in $\text{kg m/s}$. It has the direction of the velocity.

A light thing moving fast can have the same momentum as a heavy thing moving slowly.

You should find that the car's line is far steeper: each m/s gives it much more momentum. Even so, a slow enough car can have less momentum than the cyclist.

Watch out. Momentum has a direction. A ball moving left has negative momentum if right is plus, so a bounce changes the momentum by the sum of the two speeds times the mass.

A worked example

Find the momentum of a $0.16\ \text{kg}$ cricket ball at $35\ \text{m/s}$, a $70\ \text{kg}$ sprinter at $9\ \text{m/s}$, and a $1400\ \text{kg}$ car at $2\ \text{m/s}$.

1. Ball. $0.16\ \text{kg} \times 35\ \text{m/s} = 5.6\ \text{kg m/s}$.
2. Sprinter. $70\ \text{kg} \times 9\ \text{m/s} = 630\ \text{kg m/s}$.
3. Car. $1400\ \text{kg} \times 2\ \text{m/s} = 2800\ \text{kg m/s}$: the slow car has the most.

Practise with new numbers

Try it in Python

The program works out the three momenta.

Remember these

• $p = mv$, in $\text{kg m/s}$, with a direction.
• More mass or more speed means more momentum.
• A reversal changes the momentum by $m(u + v)$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. What is the momentum of a $50\ \text{kg}$ girl running at $4\ \text{m/s}$?

2. What is the momentum of a parked bus?

3. A $2\ \text{kg}$ trolley has a momentum of $12\ \text{kg m/s}$. How fast is it moving?

4. Two balls have the same momentum. One has twice the mass of the other. How do their speeds compare?