A flywheel whose moment of inertia about its axis of rotation is 16kg/m2 is rotating freely in its own plane about a smooth axis through its center. Its angular velocit is 9 rad/s when a torque is applied to bring it to rest in t0 second. Find 0t if

a)the torque is constant(=4Nm)

b)the magnitude of the torque after t secnds is given by kt.

torque = I(alfa)

case 1) I(alfa) = 4

           alfa = 4/I =4/16 = 0.25rad/s²

  for constant torque we can apply , w = w_i + (alfa)t

      since torque is retarding so w = w_i-(alfa)t

         final body stops so w = 0  ,   w_i=9rad/sec (given)

                      t = alfa/w_i = 0.25/9 = 0.0277sec

case2) torque = I(alfa)                                  

       alfa = kt/I = -kt/16                        (when k > 0 )

      alfa = dw/dt

      dw/dt = -kt/16

     w = -kt²/32 + c                   (c is constant of integration)

   at t=0 , w = 9 , putting this in above expression

     c = 9

  w = -kt²/32+ 9

  when body comes to rest then w = 0

 t = (32*9/k)^1/2 = 12root(2/k)