# Momentum (physics)

Momentum and inertia are related. Inertia is the tendency for a body to remain at rest, until and unless a force makes it begin moving. That same tendency works when it is in motion.

The motion of an object will continue until something makes it change its motion. A railroad car, once it gets going, will continue its motion for a long time, until the tiny forces of friction cause it to slow down and stop. This can take miles. Even putting on the brakes can take up to mile, because there is so much momentum.

Momentum is defined in Physics as the product (p) of a body's mass and velocity.

The faster it goes, the more momentum it has. The more it weighs, the more momentum it has.

A force in the same direction as the body is moving, will increase its speed. A force in the opposite direction will slow it down.

A force coming from the side will turn it.

An interesting case of a sideways force is a weight on the end of a string (like the Biblical slingshot used by David against Goliath). While the weight is revolving around you, the string is pulling the weight toward you - but it never gets any closer! This is called a centripetal, or center seeking, force.

### Generalized momentum

The definition of momentum can be generalized in Lagrangian and Hamiltonian dynamics, to

where L is the Lagrangian and is the velocity. In some cases the generalized momentum is the same as the momentum defined above. For example, for a free particle the Lagrangian equals the kinetic energy and so

as above.