Set 8 Problem number 16

• Important Note on Notation

• Problem

• Solution

• Generalized Solution

• Explanation in terms of Figure(s); Extension

• Figure

Problem

During a 1.7 -second time interval, a disk is observed to accelerate from 6.2 radians/second to 9.900001 radians/second.

• If the net torque on the disk is known to have been 2.8 meter Newtons, what must have been the moment of inertia of the disk?

Solution

The information given implies an angular acceleration of 2.176471 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

= ( 2.8 meter Newtons)/( 2.176471 radians/second ^ 2)

= 1.286486 kg m ^ 2/s ^ 2/(rad/s ^ 2)

= 1.286486 kg m ^ 2.