Momentum and forces

There’s a special link between the momentum of an object and the forces which act on the object.

If we apply a force of newtons to an object, for seconds, the change in momentum of the object (the impulse) is the force multiplied by the time for which the force is applied:

Change in momentum

If we replace the word impulse with the change in momentum, we can write the equation like this:

The full equation

We know that the equation for momentum is:

That means we can replace for momentum with in the first equation here:

You may see this rewritten as:

Where:

• is the force in newtons ()
• is the change in momentum in kilogram meters per second (). Otherwise known as the impulse.
• is the time for which the force is applied in seconds ()

Force-time graphs

If we plot a graph with force on the y-axis and time on the x-axis:

• The y-axis will show the force, in Newtons ()
• The x-axis will show the time, in seconds ()
• We know that one Newton is one kilogram meter per second squared () because a Newton is the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.
• So if we multiply the y-axis (force) by the x-axis (time), we get kilogram meters per second (), which is the unit for momentum!

That shows that:

The area under a force-time graph is equal to the change in momentum (or impulse) of the object.