292
Chapter 10
Rotation of a Rigid Object
About a Fixed Axis
CHAPTE R OUTLI N E
10.1
Angular Position, Velocity,
and Acceleration
10.2
Rotational Kinematics:
Rotational Motion with
Constant Angular Acceleration
10.3
Angular and Linear Quantities
10.4
Rotational Kinetic Energy
10.5
Calculation of Moments
of Inertia
10.6
Torque
10.7
Relationship Between Torque
and Angular Acceleration
10.8
Work, Power, and Energy in
Rotational Motion
10.9
Rolling Motion of a Rigid
Object
▲
The Malaysian pastime of
gasing
involves the spinning of tops that can have masses up
to 20 kg. Professional spinners can spin their tops so that they might rotate for hours before
stopping. We will study the rotational motion of objects such as these tops in this chapter.
(Courtesy Tourism Malaysia)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
293
W
hen an extended object such as a wheel rotates about its axis, the motion cannot
be analyzed by treating the object as a particle because at any given time different parts
of the object have different linear velocities and linear accelerations. We can, however,
analyze the motion by considering an extended object to be composed of a collection
of particles, each of which has its own linear velocity and linear acceleration.
In dealing with a rotating object, analysis is greatly simplified by assuming that the
object is rigid. A
rigid object
is one that is nondeformable—that is, the relative loca
tions of all particles of which the object is composed remain constant. All real objects
are deformable to some extent; however, our rigidobject model is useful in many situa
tions in which deformation is negligible.
10.1
Angular Position, Velocity, and Acceleration
Figure 10.1 illustrates an overhead view of a rotating compact disc. The disc is rotating
about a fixed axis through
O
. The axis is perpendicular to the plane of the figure. Let
us investigate the motion of only one of the millions of “particles” making up the disc.
A particle at
P
is at a fixed distance
r
from the origin and rotates about it in a circle of
radius
r
. (In fact,
every
particle on the disc undergoes circular motion about
O
.) It is
convenient to represent the position of
P
with its polar coordinates (
r
, ), where
r
is
the distance from the origin to
P
and
is measured
counterclockwise
from some
reference line as shown in Figure 10.1a. In this representation, the only coordinate
for the particle that changes in time is the angle
;
r
remains constant. As the particle
moves along the circle from the reference line (
0), it moves through an arc of
length
s
, as in Figure 10.1b. The arc length
s
is related to the angle
through the
relationship
(10.1a)
(10.1b)
Note the dimensions of
in Equation 10.1b. Because
is the ratio of an arc length
and the radius of the circle, it is a pure number. However, we commonly give
the arti
ficial unit
radian
(rad), where
Because the circumference of a circle is 2
corresponds to an angle of (2
one radian is the angle subtended by an arc length equal to the radius of the arc.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 WANG
 Acceleration, Kinetic Energy, Moment Of Inertia, Rotation, rigid object

Click to edit the document details