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(Chris Devlin) #1

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:
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