Two discs A and B are mounted coaxially on a vertical axle.The discs have moments of inertia I and 2Iabout the common axis.Disc A is imparted an initial angular velocity 2ω and disc B is imparted an angular velocity ω. Both discs rotate in clockwise direction.
Q1) When disc B is brought in contact with disc A,they acquire a common angular velocity in time t. Find the average frictional torque on one disc by the other during this period.
Q2)Find the loss in kinetic energy during above process.
1average of any quantity Q over time t= (1/t)∫Qdt
here et at any instant frictional torque be Q
then
dL/dt=Q
or
Qdt=dL
∫Qdt=Lf-L0
finally there will be no slipping and hence same angular velocities
conserving angular momentum
I2w + 2Iw = (I+2I)w'
gives w'=(4w/3)
thus Lf(of let A)-L0 = 2I(4w/3)-2I(w)=2Iw/3
thus
∫Qdt=2Iw/3 hence (1/t)∫Qdt =2Iw/3t
loss of kinetic energy =
I(4w/3)2/2 + 2I(4w/3)2/2 - I(2w)2/2-2I(w)2/2
= -Iw2/3 thus loss = Iw2/3
