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.

Question

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.

vikas askiitian expert · Answer

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)

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