A disk lying on the XY plane rinitially roates counter-clockwise with a rotational speed of w0. After a time interval rt, the rotational speed has changed to wf moving in the clockwise direction. The average torque during this time interval is which of the following?
To determine the average torque during the time interval, we need to use the equation for torque:
Torque = Moment of inertia * Angular acceleration
We can also use the equation for angular acceleration:
Angular acceleration = (Change in angular velocity) / (Time)
Given:
Initial angular velocity = w0 (counter-clockwise)
Final angular velocity = wf (clockwise)
Time interval = rt
First, let's find the change in angular velocity:
Change in angular velocity = Final angular velocity - Initial angular velocity
Change in angular velocity = wf - w0
Now, let's substitute this value into the equation for average torque:
Average torque = Moment of inertia * (Change in angular velocity / Time)
Average torque = Moment of inertia * (wf - w0) / rt
Therefore, the average torque during the time interval is Moment of inertia * (wf - w0) / rt.