Momentum is how much something wants to keep moving in the same direction.

This truck would be hard to stop ...
... it has a lot of momentum.

Faster? More momentum!
More momentum!

Momentum is mass times velocity.
The symbol is p:

p = m v

car moving

Example: What is the momentum of a 1500 kg car going at highway speed of 28 m/s (about 100 km/h or 60 mph)?

p = m v

p = 1500 kg × 28 m/s

p = 42,000 kg m/s

The unit for momentum is:

They are the same! 1 kg m/s = 1 N s

We will use both here.

More examples:

Bullet (9 mm)7.5 g
0.0075 kg

1000 m/s

0.0075 × 1000 = 7.5 kg m/s
Tennis Ball57 g
0.057 kg

50 m/s

0.057 × 50 = 2.85 kg m/s
Soccer Ball16 oz
0.45 kg
100 km/h
28 m/s

0.45 × 28 = 12.6 kg m/s
Basket Ball22 oz
0.6 kg

3 m/s

0.6 × 3 = 1.8 kg m/s
Hammer400 g
0.4 kg

7 m/s

0.4 × 7 = 2.8 kg m/s
80 kg
9 km/h
2.5 m/s

80 × 2.5 = 200 kg m/s
1500 kg
100 km/h
28 m/s

1500 × 28 = 42,000 kg m/s

Momentum has direction: the exact same direction as the velocity.

But many examples here only use speed (velocity without direction) to keep it simple.


Impulse is change in momentum. Δ is the symbol for "change in", so:

Impulse is Δp

Force can be calculated from the change in momentum over time (called the "time rate of change" of momentum):

F = ΔpΔt

brick wall

Example: You are 60 kg and run at 3 m/s into a wall.

The wall stops you in 0.05 s. What is the force?

The wall is then padded and stops you in 0.2 s. What is the force?

First calculate the impulse:

Δp = m v

Δp = 60 kg x 3 m/s

Δp = 180 kg m/s

Stopping in 0.05 s:

F = ΔpΔt

F = 180 kg m/s0.05 s = 3600 N

Stopping in 0.2 s:

F = ΔpΔt

F = 180 kg m/s0.2 s = 900 N

Stopping at a slower rate has much less force!

Q: Isn't force normally calculated using F = ma ?
A: Well, F = ΔpΔt is the same thing, just a different form:

Start with: F = ma
Acceleration is change in velocity v over time t: F = mΔvΔt
Rearrange to: F = ΔmvΔt
And Δmv is change in momentum: F = ΔpΔt

Impulse From Force

We can rearrange:

F = ΔpΔt


Δp = F Δt

So we can calculate the Impulse (the change in momentum) from force applied for a period of time.

Example: A ball is hit with a 300 N force. High speed cameras show the contact lasted for 0.02 s. What was the impulse?

Δp = F Δt

Δp = 300 N × 0.02 s

Δp = 6 N s

Momentum is Conserved

Conserved: the total stays the same (within a closed system).


Closed System: nothing transfers in or out, and no external force acts on it.

In our Universe:

Note: At an atomic level Mass and Energy can be converted via E=mc2, but nothing gets lost.

Momentum is a Vector

Momentum is a vector: it has size AND direction.

vector magnitude and direction

Sometimes we don't mention the direction, but other times it is important!

One Dimension

A question may have only one dimension, and all we need is positive or negative momentum:

negative positive

Two or More Dimensions

Questions can be in two (or more) dimensions like this one:

ball bounces at 50 degrees

Example: A pool ball bounces!

It hits the edge with a velocity of 8 m/s at 50°, and bounces off at the same speed and reflected angle.

It weighs 0.16 kg. What is the change in momentum?

Let's break the velocity into x and y parts. Before the bounce:

After the bounce:

The x-velocity does not change, but the y-velocity changes by:

Δvy = (8+8) × sin(50°)
= 16 × sin(50°)

And the change in momentum is:

Δp = m Δv

Δp = 0.16 kg × 16 × sin(50°) m/s

Δp = 1.961... kg m/s

momentum animation thumbnail


Play with momentum in this animation.


Footnote: The formula

p = m v
Momentum is mass times velocity

is not the full story!

It is a wonderful and useful formula for normal every day use, but when we look at the atomic scale things don't actually collide. They interact from a distance through electro-magnetic fields.

And the interaction does not need mass, because light (which has no mass) can have momentum.