There are two kinds of momentum, linear and angular. A spinning object has angular momentum; an object traveling with a velocity has linear momentum. We'll focus on linear momentum for now, and just refer to it as momentum.

The symbol for momentum is p.

Four fast facts about momentum

1. p = mv
   
   
2. Momentum is a vector, pointing in the direction of the velocity.
   
   
3. If there is no net force acting on a system, the system's momentum is conserved.
   
   
4. A net force produces a change in momentum that is equal to the force multiplied by the time interval during which the force was applied.

   Impulse

   Newton originally wrote his Second Law of Motion in terms of momentum, as what we now call the impulse equation. Impulse is the product of a force and the time interval over which the force acts.

   Remember that work (a force acting over a distance) produces a change in kinetic energy. An impulse (a force acting over a time interval) produces a change in momentum.

   F = ma

   F

   =

   m

   dv dt

   =

   d(mv) dt

   =

   dp dt

   Expressed as an integral, this becomes:

   ∫ F dt = Δp

   The impulse, which is the change in momentum, is the area under the force vs. time graph.

   Impulse example

   A hose sprays water directly at a wall. If the volume of water emerging from the hose is X liters/second, and the water has velocity v, directed horizontally, how much force is exerted on the wall by the water?

   Assume that the water does not bounce back, but is simply stopped by the wall. Focus on one second worth of water. X liters has a mass of X kg, so the momentum of the water goes from Xv to zero, a change of -Xv. To produce this change in momentum, the wall must exert a force on the water of -Xv newtons. The water exerts an equal and opposite force on the wall, Xv newtons in the direction the hose points.

   If v = 10 m/s and X is 3 liters/second, the force has a magnitude of 30 N.