Actually this is an ambiguous question as there are several velocities and several laws that govern them.
There is the angular velocity; for example w = 2pi radians/minute, which is the same as 1 rpm. There is also the tangential or linear velocity v = wr, where r is the radius of gyration and w is still the angular velocity. That is V = wR > wr = v because the radius R is bigger than r < R.
Unless a net force is applied to the merry go round, the angular velocity w remains fixed. It's the same throughout. But as the linear velocity depends on the distance r from the axis of rotation, v varies. It grows for a given w as we move outward from the center of the turn.
So that's one relationship where the velocity increases. Just move outward from the axis of rotation.
In other cases, we make some changes to the system. For example, we can push on the MGM to make it go faster. And that happens because we add energy, work energy (QE), by the push. And QE = dKE = 1/2 km (v^2 - u^2) which is the change in angular kinetic energy and the speed goes up from u to v > u.
Or we could move a weight m inward towards the rotation axis; say from R to r < R radius. In which case, from the conservation of momentum law, we have I(R)w = I(r)W as the angular momenta before (R) and after (r) the move. The I's are the moments of inertia for the MGM with a weight m aboard. Simple physics would show that to conserve the initial momentum at R the angular speed would need to increase from w to W > w when moving in to r < R.
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Actually this is an ambiguous question as there are several velocities and several laws that govern them.
There is the angular velocity; for example w = 2pi radians/minute, which is the same as 1 rpm. There is also the tangential or linear velocity v = wr, where r is the radius of gyration and w is still the angular velocity. That is V = wR > wr = v because the radius R is bigger than r < R.
Unless a net force is applied to the merry go round, the angular velocity w remains fixed. It's the same throughout. But as the linear velocity depends on the distance r from the axis of rotation, v varies. It grows for a given w as we move outward from the center of the turn.
So that's one relationship where the velocity increases. Just move outward from the axis of rotation.
In other cases, we make some changes to the system. For example, we can push on the MGM to make it go faster. And that happens because we add energy, work energy (QE), by the push. And QE = dKE = 1/2 km (v^2 - u^2) which is the change in angular kinetic energy and the speed goes up from u to v > u.
Or we could move a weight m inward towards the rotation axis; say from R to r < R radius. In which case, from the conservation of momentum law, we have I(R)w = I(r)W as the angular momenta before (R) and after (r) the move. The I's are the moments of inertia for the MGM with a weight m aboard. Simple physics would show that to conserve the initial momentum at R the angular speed would need to increase from w to W > w when moving in to r < R.