[Physics] Increase in kinetic energy as some one walks to the centre of a merry-go-round

forcesrotationrotational-dynamics

When someone walks to the directly centre of a merry-go-round the total kinetic energy of the merry-go-round and person system increases. (assuming the kinetic energy due to the person walking to the centre (i.e. their radial) kinetic energy is negligible). I understood that this extra energy comes from the person doing work on the merry-go-round but how can this be? They are providing no work to the merry-go-round in the direction of its motion and thus doing no work on it. So how does the work get transverse from chemical energy in the persons muscles to the kinetic energy of the merry-go-round person system (assuming the person starts and ends at rest with respect to the merry-go-round). (I also know that we need this increases in energy to satisfy the principle of the conservation of angular momentum ). Thanks.

Best Answer

Working in the frame of reference of the ground:

As the person walks towards the center of the merry-go-round, their tangential velocity decreases: from a high value at the rim to close to zero when they reach the center.

Thus, there must be a tangential force acting on the walker to reduce their tangential velocity; it comes from the force of friction between their feet and the surface of the merry-go-round. The tangential reaction force exerted by their feet on the surface of the merry-go-round acts to increase the angular velocity and kinetic energy of the structure...

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