Angular velocity of cylinders after slipping over each other

[carlyn medona]

Homework Statement

two cylinders of radii r1, and r2
having moments of inertia I1, and I2, about their
respective axes. Initially, the cylinders rotate about their
axes with angular speeds w1, and w 2 as shown in the
figure. The cylinders are moved closer to touch each other
keeping the axes parallel. The cylinders first slip over
each other at the contact but the slipping finally ceases
due to the friction between them. Find the angular speeds
of the cylinders after the slipping ceases

Homework Equations

3. The Attempt at a Solution [/B]
I applied conservation of angular momentum for the system
so, I1w1-I2w2=I1ω1-I2ω2
since linear speed is same ω1r1=-ω2r2
so I got ω1 on solving to be=r2(I1w1-I2w2)/(I1r2-I2r1)
which is wrong,

 

[orientor]

Conservation of angular momentum cannot be applied in the axis parallel to axis of cylinder. This is because force is being applied by the axis so that F_ext=0.
and this force will generate torque about any axis parallel to the cylinder axis.

 

[haruspex]

I applied conservation of angular momentum for the system

That is only valid for a system upon which there is no net external torque. In this case, each cylinder is constrained to an axle, so the axles can exert forces on the system. You can eliminate one by taking moments about an axle, but then you have a net torque from the other axle. There's no way to eliminate both.
Consider the tangential forces the cylinders exert on each other.