9.1 Linear momentum and force

Linear momentum

The scientific definition of linear momentum is consistent with most people’s intuitive understanding of momentum: a large, fast-moving object has greater momentum than a smaller, slower object. Linear momentum is defined as the product of a system’s mass multiplied by its velocity. In symbols, linear momentum is expressed as

Momentum is directly proportional to the object’s mass and also its velocity. Thus the greater an object’s mass or the greater its velocity, the greater its momentum. Momentum $\mathbf{p}$ is a vector having the same direction as the velocity $\mathbf{\text{v}}$ . The SI unit for momentum is $\text{kg}·\text{m/s}$ .

Momentum and newton’s second law

The importance of momentum, unlike the importance of energy, was recognized early in the development of classical physics. Momentum was deemed so important that it was called the “quantity of motion.” Newton actually stated his second law of motion    in terms of momentum: The net external force equals the change in momentum of a system divided by the time over which it changes. Using symbols, this law is

where ${\mathbf{F}}_{\text{net}}$ is the net external force, $\mathrm{\Delta }\mathbf{p}$ is the change in momentum, and $\mathrm{\Delta }t$ is the change in time.