9781118230725.pdf

Linear Momentum

Here we discuss only a single particle instead of a system of particles, in order to

define two important quantities. Then we shall extend those definitions to sys-

tems of many particles.

The first definition concerns a familiar word —momentum— that has several

meanings in everyday language but only a single precise meaning in physics and

engineering. The linear momentumof a particle is a vector quantity that is

defined as

(linear momentum of a particle), (9-22)

in which mis the mass of the particle and is its velocity. (The adjective linearis of-

ten dropped, but it serves to distinguish from angularmomentum, which is intro-

duced in Chapter 11 and which is associated with rotation.) Since mis always a

positive scalar quantity, Eq. 9-22 tells us that and have the same direction. Fromp: v:

p:

:v

p:mv:

p:

224 CHAPTER 9 CENTER OF MASS AND LINEAR MOMENTUM

9-3LINEAR MOMENTUM

After reading this module, you should be able to...

9.13Identify that momentum is a vector quantity and thus has
both magnitude and direction and also components.
9.14Calculate the (linear) momentum of a particle as the
product of the particle’s mass and velocity.
9.15Calculate the change in momentum (magnitude and di-
rection) when a particle changes its speed and direction of
travel.

9.16Apply the relationship between a particle’s momentum

and the (net) force acting on the particle.

9.17Calculate the momentum of a system of particles as the

product of the system’s total mass and its center-of-mass

velocity.

9.18Apply the relationship between a system’s center-of-

mass momentum and the net force acting on the system.

●For a single particle, we define a quantity called its linear
momentum as

,

which is a vector quantity that has the same direction as the
particle’s velocity. We can write Newton’s second law in

:pmv:

:p terms of this momentum:

●For a system of particles these relations become

and F

:

net

dP

:

dt

P.

:

Mv:com

F

:

net

dp:

dt

.

Learning Objectives

Key Ideas

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)

In words, Eq. 9-23 says that the net external force on a particle changes the

particle’s linear momentum Conversely, the linear momentum can be

changed only by a net external force. If there is no net external force, cannot

change. As we shall see in Module 9-5, this last fact can be an extremely power-

ful tool in solving problems.

p:

p:.

F

:

net

F

:

net

dp:

dt

.

Eq. 9-22, the SI unit for momentum is the kilogram-meter per second (kg m/s).

Force and Momentum.Newton expressed his second law of motion in terms

of momentum: