1135
REVIEW AND SUMMARY
In this chapter we again considered the method of work and energy
and the method of impulse and momentum. In the first part of the
chapter we studied the method of work and energy and its applica
tion to the analysis of the motion of rigid bodies and systems of rigid
bodies.
In Sec. 17.2, we first expressed the principle of work and energy for
a rigid body in the form
T
1
1
U
1
y
2
5
T
2
(17.1)
where
T
1
and
T
2
represent the initial and final values of the kinetic
energy of the rigid body and
U
1
y
2
represents the work of the
external
forces
acting on the rigid body.
In Sec. 17.3, we recalled the expression found in Chap. 13 for the
work of a force
F
applied at a point
A
, namely
U
1
y
2
5
#
s
2
s
1
(
F
cos
a
)
ds
(17.3
9
)
where
F
was the magnitude of the force,
a
the angle it formed with
the direction of motion of
A
, and
s
the variable of integration mea
suring the distance traveled by
A
along its path. We also derived the
expression for the
work of a couple of moment
M
applied to a rigid
body during a rotation in
u
of the rigid body:
U
1
y
2
5
#
u
2
u
1
M
d
u
(17.5)
We then derived an expression for the kinetic energy of a rigid body
in plane motion [Sec. 17.4]. We wrote
T
5
1
2
mv
2
1
1
2
I
v
2
(17.9)
where
v
is the velocity of the mass center
G
of the body,
v
is the
angular velocity of the body, and
I
is its moment of inertia about an
axis through
G
perpendicular to the plane of reference (Fig. 17.13)
[Sample Prob. 17.3]. We noted that the kinetic energy of a rigid body
in plane motion can be separated into two parts: (1) the kinetic
energy
1
2
mv
2
associated with the motion of the mass center
G
of the
body, and (2) the kinetic energy
1
2
I
v
2
associated with the rotation of
the body about
G.
Principle of work and energy
for a rigid body
Work of a force or a couple
Kinetic energy in plane motion
G
w
Fig. 17.13
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1136
Plane Motion of Rigid Bodies: Energy and
Momentum Methods
For a rigid body rotating about a fixed axis through
O
with an angular
velocity
V
, we had
T
5
1
2
I
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 Fall '10
 IB
 Angular Momentum, Kinetic Energy, Momentum, Rigid Body

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