A moment of inertia in Patterdale

 I timed 2 circuits of the roundabout as shown below.

Then moving towards the centre, I timed again. This time each rotation was 1 second faster.

The reason is that for circular motion, it is not just mass that affects motion but distance from the middle. The combination of the two is called moment of inertia. Angular momentum is conserved in the movement to the middle. Angular momentum = moment of inertia x angular velocity. Moving towards the centre reduces the moment of inertia because it is easier to accelerate a mass closer to you in a circular motion. If momentum is conserved but moment of inertia is reduced, angular velocity must increase thus each rotation takes less time.