By Steven Holzner

Momentum is the most important quantity when it comes to handling collisions in physics. Momentum is a physical quantity defined as the product of mass multiplied by velocity. Note the definition says velocity, not speed, so momentum is a vector quantity. This means that a 1,000-kg car moving north at 20 m/s has a different momentum from a 1,000-kg car moving south at 20 m/s. The symbol for momentum symbol is p; here’s the equation for momentum:

p = mv

Note that p is always in the same direction as v because m is a scalar value (that is, a single value, not a value with multiple components like a vector). It turns out that total momentum is conserved in collisions, which means that the total momentum before a collision is the same as the momentum after a collision. For example, if two billiard balls collide on a pool table, then the momentum of the first billiard ball before the collision plus the momentum of the second billiard ball before the collision equals the momentum of the first billiard ball after the collision plus the momentum of the second billiard ball after the collision.

So if you know the original momentum in the collision, you can make predictions about the situation after the collision (and physicists are always delighted by such predictions). Conservation of momentum is particularly useful for understanding the world of particle physics.

What are the units of momentum? Momentum is mass times velocity, so its unit is kilogram x meters/second (kg-m/s) in the MKS system.

Sample question

  1. Suppose that you’re in an 800.0-kg race car going 200.0 miles an hour due east. If you have a mass of 60.0 kg, what is the total momentum?

    The correct answer is 7.7 x 104 kg-m/s, due east.

    1. Use the equation p = mv.

    2. Plug in the numbers, after first converting 200 miles per hour to 89.4 m/s:

      p = mv = (800.0 kg + 60.0 kg)(89.4 m/s) = 7.7 x 104 kg-m/s, due east.

Practice questions

  1. You’re running north at 3.0 m/s. If you have a mass of 80.0 kg, what is your momentum?

  2. You’re falling out of an airplane, and before opening your parachute, you hit a speed of 100.0 m/s. What is your momentum if you have a mass of 80.0 kg?

  3. You’re pushing a 10.0-kg box of dishes across the kitchen floor at a rate of 4.0 m/s. What is its momentum?

  4. You’re pushing an 1200.0-kg car down the road, and it’s going at 6.0 m/s west. How much momentum does it have?

Following are answers to the practice questions:

  1. 240 kg-m/s north

    1. Use the equation p = mv.

    2. Plug in the numbers:

      p = mv = (80.0 kg)(3.0 m/s) = 240 kg-m/s north

  2. 8,000 kg-m/s downward

    1. Use the equation p = mv.

    2. Plug in the numbers:

      p = mv = (80.0 kg)(100.0 m/s) = 8,000 kg-m/s downward

  3. 40 kg-m/s

    1. Use the equation p = mv.

    2. Plug in the numbers:

      p = mv = (10.0 kg)(4.0 m/s) = 40 kg-m/s

  4. 7,200 kg-m/s west

    1. Use the equation p = mv.

    2. Plug in the numbers:

      p = mv = (1200.0 kg)(6.0 m/s) = 7,200 kg-m/s west