Continuing from the following scenario from my previous question Centripetal force of a rotating rigid body? :
Consider someone pushing a roundabout in a playground. Initially the roundabout is stationary, but when it is pushed, it rotates with increasing rotational speed.
The force of the push is balanced by the reaction force exerted by the support at the centre of the roundabout. The forces are equal in magnitude and opposite in direction, so the roundabout is in translational equilibrium. But they have different lines of action, so there is a resultant torque, causing the playground to rotate and have angular momentum.
Okay, suppose the roundabout's rotational speed now stabilises (ie. the resultant torque becomes zero and the roundabout is in rotational equilibrium). I infer that this happens only when the pushing force is removed (otherwise there would be a resultant torque as described in the yellow box). But if so, what (force) is keeping the roundabout rotating at its constant rotational speed (assuming no friction)? Isn't circular/rotational motion a forced motion??