Mass times velocity.

Step 1 of 5

What momentum is

An empty shopping trolley is easy to stop by hand. The same trolley full, at the same speed, is much harder to stop. And even an empty trolley is hard to stop when it is racing down a slope. How hard a moving object is to stop depends on both its mass and its speed, together.

That quantity is called momentum: mass times velocity,

$p = mv$⁠

In the Scene cart A, 1 kg, rolls at 0.6 m/s into cart B, which stands still. Look inside is open at Momentum and energy: the board behind the track shows each cart’s momentum, and over each cart an arrow gives its mass and velocity. Change Mass of cart A and Speed of cart A, and watch A’s bar grow.

Step 2 of 5

Working out momentum

To work out momentum, multiply the mass in kilograms by the velocity in metres per second. A 1 kg cart at 0.6 m/s carries 0.6 kg·m/s.

Now cart A is heavier and faster, and the board is hidden. Work out its momentum yourself.

Step 3 of 5

Heavy and slow, light and fast

In momentum the mass and the speed count equally: a cart of twice the mass and a cart at twice the speed both carry twice the momentum. So a heavy, slow cart and a light, fast one can carry exactly the same momentum.

Step 4 of 5

Car or bullet

Momentum is not kinetic energy. Both grow with the mass and the speed, but in kinetic energy, $\tfrac12 mv^2$⁠, the speed is squared, and in momentum it is not. So a small, very fast object can carry a lot of kinetic energy and little momentum.

Step 5 of 5

Momentum has a direction

Velocity is a vector: it has a size and a direction. So does momentum. On a straight track a sign is enough: take right as positive, and the momentum of a cart moving left is negative.

Now cart B is twice as heavy as A, and the collision is perfectly bouncy. Watch cart A after the hit: it does not stop, it comes back.