0.1 6.2 linear momentum and force  (Page 2/4)

This statement of Newton’s second law of motion includes the more familiar ${\mathbf{F}}_{\text{net}}\text{=}m\mathbf{a}$ as a special case. We can derive this form as follows. First, note that the change in momentum $\mathrm{\Delta }\mathbf{p}$ is given by

If the mass of the system is constant, then

So that for constant mass, Newton’s second law of motion becomes

Because $\frac{\mathrm{\Delta }\mathbf{v}}{\mathrm{\Delta }t}=\mathbf{a}$ , we get the familiar equation

when the mass of the system is constant .

Newton’s second law of motion stated in terms of momentum is more generally applicable because it can be applied to systems where the mass is changing, such as rockets, as well as to systems of constant mass. We will consider systems with varying mass in some detail ; however, the relationship between momentum and force remains useful when mass is constant, such as in the following example.

Section summary

• Linear momentum ( momentum for brevity) is defined as the product of a system’s mass multiplied by its velocity.
• In symbols, linear momentum $\mathbf{p}$ is defined to be
  $\mathbf{p}=m\mathbf{v},$
  where $m$ is the mass of the system and $\mathbf{v}$ is its velocity.
• The SI unit for momentum is $\text{kg}·\text{m/s}$ .
• Newton’s second law of motion in terms of momentum states that the net external force equals the change in momentum of a system divided by the time over which it changes.
• In symbols, Newton’s second law of motion is defined to be
  ${\mathbf{F}}_{\text{net}}=\frac{\mathrm{\Delta }\mathbf{p}}{\mathrm{\Delta }t}\text{,}$
  ${\mathbf{F}}_{\text{net}}$ is the net external force, $\mathrm{\Delta }\mathbf{p}$ is the change in momentum, and $\mathrm{\Delta }t$ is the change time.

Conceptual questions

Problems&Exercises