# Conservation of Angular Momentum in different cases

Conservation of angular momentum can be applied when there is no external torque on the system which is isolated. However, my physics teacher gives me a sum that:

Two discs are pressed against each other until they stop slipping on each other. Find angular speed of the bigger disc when they stop slipping. Disc 1 (mass $$m$$, radius $$r$$) and disc 2 (mass $$m/2$$, radius $$2r$$). Disc 1 had angular speed $$\omega$$ initially, whereas disc 2 was at rest initially.

I tried to apply the law of conservation of angular momentum in this case since there is no external torque, but my teacher says that angular momentum is not conserved since there is an external torque acting on it. I fail to understand what is the external torque in this case. I don't need the answer to this question, but the reason why the law of conservation of angular momentum cannot be applied, and what is the external torque that acts on this body?

Look at the left hand diagram which has the two frictional, equal magnitude and opposite direction. forces (red) acting on the discs.

There are no external forces but each disc has a net force on it and so the centre of mass of each disc will undergo a translation acceleration.

To stop that translational acceleration of the centres of mass of the two discs forces (blue) must be applied to the axles of the discs and these are external forces for a system which is defined to be just the two discs.

Note that there are similar problems where the two discs share a common axis of rotation.
In that case conservation of angular momentum can be used.

• Excellent answer, sir! Just like the pulley system in which the support attached to the pulley gives some force to balance it in the air, the hinges over here provide force for stopping the translation acceleration. – Siddharth Venu Mar 7 '17 at 9:01
• @Farcher But do these forces exert a net torque along the axis of rotation? I mean shouldn't their torque equal zero as the pass through the axis so the angular momentum is conserved along the axis of rotation? – Antonios Sarikas Dec 29 '20 at 20:51
• There is an external torque (due to the blue couple) acting on the system of magnitude $F(r+2r) = 3Fr$ and it is in an anticlockwise direction. – Farcher Dec 30 '20 at 0:06