Linear Momentum

Momentum is a word that has several meanings in everyday language but only a single precise meaning in physics. The linear momentumof a particle is a vector defined as

in which is the mass of the particle and is its velocity. (The adjective linear is often dropped, but it serves to distinguish from angular momentum, which is associated with rotation.) Since is always a positive scalar quantity, Eq. 9-22 tells us that and have the same direction. From Eq. 9-22, the SI unit for momentum is the kilogram-meter per second.

Newton actually expressed his second law of motion in terms of momentum:

The time rate of change of the momentum of a particle is equal to the net force acting on the particle and is in the direction of that force.

In equation form this becomes

(9-23)

Substituting for from Eq. 9-22 gives

Thus, the relations and are equivalent expressions of Newton's second law of motion for a particle. Thus, the relations and are equivalent expressions of Newton's second law of motion for a particle.

•Checkpoint 3:The figure gives the linear momentum versus time for a particle moving along an axis. A force directed along the axis acts on the particle, (a) Rank the four regions indicated according to the magnitude of the force, greatest first, (b) In which region is the particle slowing?