A disk, initially rotating at 146 rad/s, is slowed down with a constant angular acceleration of magnitude 4.55 rad/s2. (a) How much time does the disk take to stop? (b) Through what angle (rad) does the disk rotate during that time?

a) 32.1 s

b) 2342 rad

Explanation:

a)

To solve this problem, we can use the equivalent of the suvat equations for a rotational motion.

In fact, the motion of the disk is a rotational motion with unifom angular acceleration.

So we can use the following suvat equation:

where:

is the initial angular velocity

is the final angular velocity

is the angular acceleration

t is the time elapsed

In this problem:

is the initial angular velocity

, since the disk comes to a stop

(negative since the disk is slowing down)

Therefore, the time taken to stop is

b)

To solve this part of the problem, we can use another suvat equation for the rotational motion, which is:

where

is the initial angular velocity

is the angular acceleration

t is the time elapsed

is the angular displacement covered

For the disk in this problem:

is the initial angular velocity

(negative since the disk is slowing down)

t = 32.1 s (time elapsed, found in part a)

Substituting, we find the angle through which the disk has rotated in this time: