Question

A professor, with dumbbells in his hands and holding his arms out, is spinning on a turntable with an angular velocity. What happens after he pulls his arms inwards

Answer 1

His angular velocity will increase.

Step-by-step explanation:

According to the conservation of rotational momentum, the initial angular momentum of a system must be equal to the final angular momentum of the system.

The angular momentum of a system =
`I`'ω'

where

`I`' is the initial rotational inertia

ω' is the initial angular velocity

the rotational inertia =
`mr'^(2)`

where m is the mass of the system

and r' is the initial radius of rotation

Note that the professor does not change his position about the axis of rotation, so we are working relative to the dumbbells.

we can see that with the mass of the dumbbells remaining constant, if we reduce the radius of rotation of the dumbbells to r, the rotational inertia will reduce to
`I`.

From

`I`'ω' =
`I`ω

since
`I` is now reduced, ω will be greater than ω'

therefore, the angular velocity increases.