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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 w2 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.
I applied conservation of momentum here but I'm unable to obtain the right answer. Taking both cylinders as system, since only friction acts and these forces contribute to internal torques so with absence of external torques I conserved angular momentum of the system but the answer is incorrect.
My question is why cant we conserve angular momentum in such a scenario? How is there external torque and what forces are providing the external torque?