A rotating wheel has a constant angular acceleration. It has an angular velocity of 5.0 rad/s at time t = 0 s, and 3.0 s later has an angular velocity of 9.0 rad/s. What is the angular displacement of the wheel during the 3.0-s interval?

Angular displacement during 3 seconds is 21 rad

Explanation:

We have equation of motion v = u + at

Initial velocity, u = 5 rad/s

Final velocity, v = 9 rad/s

Time, t = 3 s

Substituting

v = u + at

9 = 5 + a x 3

a = 1.33 rad/s²

Angular acceleration is 1.33 rad/s²

Now we have equation of motion v² = u² + 2as

Initial velocity, u = 5 rad/s

Final velocity, v = 9 rad/s

Angular acceleration = 1.33 rad/s²

Substituting

v² = u² + 2as

9² = 5² + 2 x 1.33 x s

s = 21 radians

Angular displacement during 3 seconds is 21 rad