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This question is about the conservation of angular momentum:

So far, I have understood the reason as to why an object with a high moment of inertia has a small angular acceleration whereas an object with a low moment of inertia has a larger angular acceleration. The reason for this is that if there are high values of r, the moment of inertia will be larger and hence a larger effort (to produce a larger torque) must be exerted. As a result, the angular acceleration of the object is small. This can be demonstrated in (a) where the change in omega/time is small

In example (b) shown above, the ballerina takes advantage of the moment of inertia by not stretching her hands out etc. and by doing so decreasing the moment of inertia and therefore a smaller torque is produced to rotate at a faster rate.

However, what I can't fathom out is; how is this related to the conservation of angular momentum which states that angular momentum is conserved unless there are external torques acting on the system.

I appreciate your comments about this and any other solutions as to why a ballerina rings in her arms and legs to spin. Thanks a lot!

So far, I have understood the reason as to why an object with a high moment of inertia has a small angular acceleration whereas an object with a low moment of inertia has a larger angular acceleration. The reason for this is that if there are high values of r, the moment of inertia will be larger and hence a larger effort (to produce a larger torque) must be exerted. As a result, the angular acceleration of the object is small. This can be demonstrated in (a) where the change in omega/time is small

In example (b) shown above, the ballerina takes advantage of the moment of inertia by not stretching her hands out etc. and by doing so decreasing the moment of inertia and therefore a smaller torque is produced to rotate at a faster rate.

However, what I can't fathom out is; how is this related to the conservation of angular momentum which states that angular momentum is conserved unless there are external torques acting on the system.

I appreciate your comments about this and any other solutions as to why a ballerina rings in her arms and legs to spin. Thanks a lot!