A disk of radius 10 cm speeds up from rest. it turns 60 radians reaching an angular velocity of 15 rad/s. what was the angular acceleration? b. how long did it take the disk to reach this velocity?​

a) The angular acceleration is 1.875 radians per square second.

b) The time taken by the disk to reach the final angular speed is 8 seconds.

Explanation:

a) Let suppose that the disk accelerates uniformly, given that initial and final angular speed (, ), in radians per second, and change in angular position (), in radians, are known. The angular acceleration (), in radians per square second, are found by using this expression:

(1)

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

The angular acceleration is 1.875 radians per square second.

b) The time taken by the disk to reach the final angular velocity is determined by the following kinematic formula:

(2)

Where is the time, in seconds.

If we know that , and , then the time taken by the disk is:

The time taken by the disk to reach the final angular speed is 8 seconds.