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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 = 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)
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)
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