← Momentum and impulse

Momentum is mass times velocity

A 2.0 kg cart rolls along a lab track at 3.0 m/s. You have seen the two things that make a mover hard to stop: its mass, and its speed.

One quantity measures the two together. What is it?

You have seen that more mass makes a mover harder to stop, and that more speed does too.

Here is the lab cart again: mass 2.0 kg, velocity 3.0 m/s. One number should measure how hard it is to stop.

Multiply the mass by the velocity: 2.0 × 3.0 = 6.0. That single number counts both.

The lab cartcasemassvelocitymomentumthe cart2.0 kg3.0 m/s6.0 kg·m/s
Multiply the mass by the velocity: the cart's momentum.

One equation says that move for every object.

momentum = mass × velocity

In symbols: p = mv.

The product mv measures how hard a moving object is to stop. This product is called the object's momentum.

Symbol keysymbolmeaningunitpmomentumkg·m/smmasskgvvelocitym/s
p = mv, each symbol labeled with its meaning and unit.

With mass in kilograms and velocity in meters per second, the cart's momentum is written 6.0 kg·m/s.

A 3.0 kg wagon rolls at 2.5 m/s. Enter its momentum in kg·m/s.

More mass means more momentum. More velocity means more momentum. And more momentum means harder to stop.

Double the masscasemassvelocitymomentumcart with double the mass4.0 kg3.0 m/s12 kg·m/s
Double the mass, same speed: double the momentum.
Double the speed insteadcasemassvelocitymomentumthe cart at double the speed2.0 kg6.0 m/s12 kg·m/s
Same mass, double the speed: double the momentum again.

Celia says: 'Of two rolling carts, the one with more momentum is harder to stop.' Is Celia correct?

Momentum's symbol is a lowercase p. Later in the course, a capital P will name power, so where the two could meet, this course writes the word power out in full.

Mass multiplied by velocity measures how hard a moving object is to stop. The product is called the object's momentum: p = mv.

A 0.60 kg basketball moves at 5.0 m/s. State its momentum.

Write down the values:

m = 0.60 kg, v = 5.0 m/s, p = ?

Write down the equation:

p = mv

Substitute in the values, and calculate:

p = 0.60 × 5.0 = 3.0

The basketball's momentum is 3.0 kg·m/s.

The same basketball is passed faster, at 8.0 m/s. State its momentum now.

Write down the values:

m = 0.60 kg, v = 8.0 m/s, p = ?

Write down the equation:

p = mv

Substitute in the values, and calculate:

p = 0.60 × 8.0 = 4.8

The basketball's momentum is now 4.8 kg·m/s. More speed, more momentum.

Your turn

A 55 kg sprinter runs at 9.0 m/s. Enter the sprinter's momentum in kg·m/s.

Which statement says what an object's momentum is?

Two identical 20 kg carts roll along a hallway, one at 4.0 m/s and one at 2.0 m/s. Which statement is correct?

Mass multiplied by velocity measures how hard a moving object is to stop. What is this product called?