Question

After fixing a flat tire on a bicycle you give the wheel a spin. Its initial angular speed was 5.45

rad/s

and it rotated 15.6 revolutions before coming to rest.

What was its average angular acceleration?

Express your answer using three significant figures.

For what length of time did the wheel rotate?

Express your answer using three significant figures.

Answer 1

Given
initial angular speed is W0 = 5.45 rad/s

   angular displacement before coming to rest is theta = 15.6*2pi rad

average angular acceleration is

  
       using equations of motion w^2 -W0^2 = 2alpha*theta
  
                   Alpha = (0-5.45^2)/2(15.6*2pi) rad/s2
                       = -0.1515160 rad/s2

For what length of time did the wheel rotate

           theta = w0t+0.5 *alpha*t^2
          
           15.6*2pi = 5.45*t+0.5(-0.1515160)*t^2
           t = 35.9815 s