With the aid of a string, a gyroscope is accelerated from rest to 32 rad/s in 0.40 s. What is its angular acceleration in rad/s2? How many revolutions does it go through in the process?

Explanation:

We have equation of motion v = u + at

     Initial angular velocity, u = 0 rad/s

     Final angular velocity, v = 32 rad/s    

     Time, t = 0.40 s

     Substituting

                      v = u + at  

                      32 = 0 + a x 0.40

                      a = 80 rad/s²

     Angular acceleration is 80 rad/s²

  We have equation of motion s = ut + 0.5 at²

        Initial angular velocity, u = 0 rad/s

        Angular acceleration, a = 80 rad/s²

        Time, t = 0.4 s      

     Substituting

                      s = ut + 0.5 at²

                      s = 0 x 0.4 + 0.5 x 80 x 0.4²

                      s = 6.4 rad

      Angular displacement  = 6.4 rad

Number of revolutions undergone is 1.02