Is impulse a vector or a scalar?

Impulse is a vector quantity, meaning it has both a magnitude and a direction. Its direction is always exactly the same as the direction of the applied force.

Are impulse and momentum the same thing?

They are closely related but not exactly the same. Momentum is a property an object has right now due to its mass and velocity. Impulse is the change in that momentum transferred to the object by a force over time.

Why are the units for impulse and momentum different?

Actually, they are fundamentally the same! Impulse is typically written as Newton-seconds ($N \cdot s$), while momentum is usually kilograms times meters per second ($kg \cdot m/s$). Because one Newton is mathematically equal to one $kg \cdot m/s^2$, the units simplify to be completely identical.

What is impulse?

Impulse is a measure of how much a force changes the momentum of an object over a specific period of time. If you think of momentum as how hard it is to stop a moving object, impulse is the push that actually changes that motion. It answers the question of what happens when you apply a force for a certain duration. By combining how hard you push with how long you push, impulse tells you exactly how much the object's speed and direction will change. It is directly equal to the object's change in momentum.

The impulse formula

In physics, impulse is represented by the symbol $J$ . The simplest way to calculate impulse is to multiply the average force ( $F$ ) by the time interval ( $\Delta t$ ) that the force is applied. This gives us the equation $J = F \Delta t$ . Because force is measured in Newtons and time in seconds, the standard unit for impulse is the Newton-second ( $N \cdot s$ ).

Pushing a broken-down car

Imagine you are trying to push a broken-down car to get it rolling. If you give it a quick, hard shove for just one second, it barely moves. But if you lean into it and push with that exact same force for ten seconds, the car picks up speed. Even though the force was identical, the longer time meant a greater impulse was delivered to the car, resulting in a much bigger change in its momentum.

The Impulse-Momentum Theorem

Impulse is incredibly useful because it equals the change in momentum of an object. This is known as the impulse-momentum theorem, written mathematically as $J = \Delta p$ , where $p$ is momentum. Since momentum is mass times velocity ( $p = m v$ ), an impulse will cause an object's mass or velocity (usually velocity) to change. This is why airbags save lives in car crashes. The total change in momentum is fixed by the car stopping, but by extending the time the collision takes, the airbag drastically reduces the peak force you feel.

Worked through

A tennis player hits a stationary 0.06 kg tennis ball. The racket is in contact with the ball for 0.005 seconds and exerts an average force of 420 Newtons. What is the impulse delivered to the ball, and what is the ball's final velocity?

First, we calculate the impulse using the force and time given. Using the formula $J = F \Delta t$ , we multiply 420 N by 0.005 s to get 2.1 N s. Next, we use the impulse-momentum theorem ( $J = \Delta p$ ) to find the final velocity. Since the ball started from rest, its initial momentum is zero, so the change in momentum is just its final mass times velocity ( $m v$ ). We set 2.1 equal to $0.06 v$ . Dividing 2.1 by 0.06 gives a final velocity of 35 m/s.

Questions students ask

Ask about this topic

Explain at

Where this comes from: OpenStax Physics Chapter 8: Linear Momentum and Collisions · Khan Academy Unit: Momentum and Impulse