Mechanics | 26307 - A flywheel whose moment of inertia about its-askIITians

rajan jha Grade: 12

        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.

8 years ago

Answers : (1)

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vikas askiitian expert

509 Points

							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)