Chapter 8
Rotational Motion

 

Center of Gravity

Example 8-17

As a grade-school 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

 

Moments-of-Inertia
Slender Rod
Slender Rod
Disk
Cylinder

Rectangular
parallelepiped

Solid Sphere
Hoop
Hoop
Spherical Shell
Cylinder
Cone
Hoop

 

Example 8-18

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 8-19

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