A rotating merry-go-round and a rocket undergoing uniform acceleration both constitute their own inertial reference frame.

No, both the rocket and the merry-go-round can not constitute inertial frame of their own

Explanation:

This can be explained as an inertial frame is one in which an object is either moving with constant velocity or is at rest and thus there won't be any acceleration acting as the velocity is constant.

In the mentioned case, both the rocket and merry-go-round are under the action of uniform acceleration, i. e., constant acceleration where the velocity changes by equal amounts in equal intervals of time and is not constant.

Therefore, they won't constitute an inertial frame of their own.