A disk of radius 25 cm spinning at a rate of 30 rpm slows to a stop over 3 seconds. What is the angular acceleration? B. How many radians did the disk turn while stopping ? C. how many revolutions? ​

A. The angular acceleration of the disk is -1.047 radians per square second.

B. The disk turns 4.715 radians while stopping.

C. The disk did 0.750 revolutions while stopping.

Explanation:

A. In this case, the disk is deceleration at a constant rate. Hence, the angular acceleration experimented by the object (), in radians per square second, can be found by means of this kinematic expression:

(1)

Where:

- Initial angular speed, in radians per second.

- Final angular speed, in radians per second.

- Time, in seconds.

If we know that , and , then the angular acceleration of the disk is:

The angular acceleration of the disk is -1.047 radians per square second.

B. The change in position of the disk (), in radians, is determined by the following kinematic formula:

(2)

If we know that , and , then the change in position is:

The disk turns 4.715 radians while stopping.

C. A revolution equals 2π radians, then, then number of revolutions done by the disk while stopping is found by simple rule of three:

The disk did 0.750 revolutions while stopping.