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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.

6 years ago

Answers : (1)

vikas askiitian expert
510 Points
										

torque = I(alfa)


case 1) I(alfa) = 4


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


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


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


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


                      t = alfa/wi = 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)


 

6 years ago
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