refraction

For the beam to rotate the source producing the light beam must be rotating.

The question does not specify if the source will continue to rotate at the same or different speed in the medium. The source does not obey the laws of refraction, so the change in its speed cannot be found using the laws of refraction.

Assuming that the speed of the source producing the light beam does not change on refraction, the angular speed of the beam will remain unchanged.