Question

A flywheel slows from 703 rev/min to 417 rev/min while rotating through 28 revolutions. What is the average angular acceleration of the flywheel during this time?

1) 10 rad/s²
2) 15 rad/s²
3) 20 rad/s²
4) 25 rad/s²

Answer 1

The average angular acceleration of the flywheel is -15 rad/s².

Step-by-step explanation:

To find the average angular acceleration of the flywheel, we need to use the equation:

Angular acceleration = (change in angular velocity) / (change in time)

First, convert the initial and final angular velocities from revolutions per minute (rev/min) to radians per second (rad/s). Then, subtract the initial angular velocity from the final angular velocity to find the change in angular velocity. Divide this by the change in time, which is the number of revolutions multiplied by the time taken for each revolution. This gives the average angular acceleration. Plugging in the given values, we get:

Angular acceleration = (417 rev/min - 703 rev/min) * (2π rad/rev) / ((28 rev) * (40s/rev)) = -15 rad/s²

Therefore, the average angular acceleration of the flywheel during this time is -15 rad/s².