Question

A flywheel slows from 600 to 400 rev/min while rotating through 40 revolutions. What is the angular acceleration of the flywheel?

Answer 1

Step-by-step explanation:

To find the angular acceleration of the flywheel, we can use the formula:

Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time

First, we need to convert the given values to radians per minute since angular velocity is typically measured in radians. There are 2π radians in one revolution.

Initial angular velocity = 600 rev/min * 2π rad/rev = 1200π rad/min

Final angular velocity = 400 rev/min * 2π rad/rev = 800π rad/min

Next, we calculate the change in angular velocity:

Change in angular velocity = Final angular velocity - Initial angular velocity

Change in angular velocity = 800π rad/min - 1200π rad/min = -400π rad/min

Finally, we divide the change in angular velocity by the number of revolutions to get the angular acceleration:

Angular acceleration = Change in angular velocity / Number of revolutions

Angular acceleration = (-400π rad/min) / 40 revolutions = -10π rad/min^2

Therefore, the angular acceleration of the flywheel is -10π rad/min^2.