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I am having a conceptual understanding with the law of Conservation of Angular momentum and when it holds.

Wikipedia says:

"In physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important quantity in physics because it is a conserved quantity – the angular momentum of a system remains constant unless acted on by an external torque."

However, I was doing a problem on a block sliding down a friction-less groove on a rigid cone, only free to rotate. It required one to find the final angular velocity when the block had reached the end. The solution said the question could be solved by noting no external torque existed in the system, so angular momentum was constant.

I thought that the external normal force between the block and the cone would produce an external torque. I am confused to why angular momentum is conserved.

Perhaps the root of my problem is that I do not fully understand what an external torque is.
Any help on the stated matters would be greatly appreciated.

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External Torque is a torque exerted by anything which is not the part of system under consideration

The question you are attempting calls for considering block and cone as one system so sum of their angular momentas about any point will always be constant

Hope this helps

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