Chapter
8
Rotational Motion
Center
of Gravity
Example
817
As
a gradeschool project, students construct a mobile representing
some of the major food groups. Their completed artwork is shown below.
Find the masses , ,
and that
are required for a perfectly balanced mobile.
Solution
The Dynamics of Rotation
Moment
of Inertia
Torque
with the moment of inertia
MomentsofInertia 








Slender
Rod 
Slender
Rod 
Disk 
Cylinder 








Rectangular parallelepiped

Solid
Sphere 
Hoop 
Hoop 








Spherical
Shell 
Cylinder 
Cone 
Hoop 
Example 818
Use
the general definition of the moment of inertia to find the moment
of inertia for the dumbbell shaped object shown below. Note the axis
of rotation goes through the center of the object and points
out of the page. In addition, assume that the masses may be treated
as point masses.
Solution:
We see that and .
Then the moment of inertia
Example 819
The
motor in an electric saw brings the circular blade from rest
up to the rated angular velocity of 80.0 rev/s in 240.0 rev.
One type of blade has a moment of inertia of .
What net torque (assumed constant) must the motor apply to the
blade?
Solution:
We need to find the angular acceleration so that we can use which
is called Newton's Second Law for rotational motion. The equation
to use to find the angular acceleration is .
Solving for :
Then
putting this expression into the torque equation and substituting:
On
to the Dynamics of Rotation 2 