Set 8 Problem number 16

• Important Note on Notation

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s); Extension

• Figure

Problem

At a certain instant a disk is rotating at 5.4 radians/second. 7 seconds later it is rotating at 11.9 radians/second.

• If it was accelerated uniformly as a result of a constant torque of 7.9 meter Newtons, then what is its moment of inertia?

Solution

The information given implies an angular acceleration of .9285713 radians/second ^ 2.

• Newton's Second Law in rotational form says that `tau = I `omega , where I is the moment of inertia, `tau is the torque and `omega is the angular acceleration.
• Since we know the angular acceleration and the torque, it is easy to find the moment of inertia.

We obtain

I = `tau / `omega

= ( 7.9 meter Newtons)/( .9285713 radians/second ^ 2)

= 8.507693 kg m ^ 2/s ^ 2/(rad/s ^ 2)

= 8.507693 kg m ^ 2.