Determining the amount of revolutions required to reach a certain angular velocity?

Question

Starting from rest, a disk takes 11 revolutions to reach an angular velocity ω at constant angular acceleration. How many additional revolutions are required to reach an angular velocity of 3ω?

____rev

Answer 1

Let:

w1 be initial angular velocity,

w2 be final angular velocity,

theta be angle of rotation,

alpha be angular acceleration,

w be the specified omega.

w2^2 = w1^2 + 2 alpha theta

Putting w1 = 0, w2 = w, theta = 11 rev:

w^2 = 2 alpha * 11

alpha = w^2 / 22

Putting w1 = w, w2 = 3w, alpha = w^2 / 22:

9w^2 = w^2 + 2w^2 theta / 22

8w^2 = w^2 theta / 11

theta / 11 = 8

theta = 88 rev.

Answer 2

22