Momentum, Impulse, Work, Energy, and Power

This lesson brings together two of the most powerful ideas in mechanics: momentum and energy. Both are conserved quantities, and conservation laws let us solve problems that would be intractable with forces alone.

Momentum and impulse

The linear momentum of an object is the product of its mass and velocity,

$$p = mv,$$

a vector measured in $\text{kg m s}^{-1}$. Newton's second law is most generally written as force equals the rate of change of momentum, $F = \Delta p / \Delta t$. Rearranging gives the impulse of a force,

$$F \Delta t = \Delta p = mv - mu.$$

Impulse, measured in $\text{N s}$, equals the change in momentum. It also equals the area under a force–time graph. This explains why crumple zones, airbags, and bending your knees when landing all reduce the force of an impact: by exte