A person of mass 55 kg stands at the center of a rotating merry-go-round platform of radius 3.4 m and moment of inertia 670 kg·m2. The platform rotates without friction with angular velocity 1.0 rad/s. The person walks radially to the edge of the platform.

Question

(a) Calculate the angular velocity when the person reaches the edge.
(b) Calculate the rotational kinetic energy of the system of platform plus person before the person's walk.
(c) Calculate the rotational kinetic energy of the system of platform plus person after the person's walk.

Please Help I have no clue where to even start! :(

Answer 1

This is a conservation of angular momentum problem.
Now, the formula for angular momentum is:
L = Iw
So basically, L before = L after:
I1w1 = I2w2
The trick to solving these is to figure out what the change in moment of inertia is, and then apply the concept of conservation of angular momentum to it.
With a person on a merry-go-round, the moment of inertia would be the moment of inertia of the person plus the moment of inertia of the merry-go-round.
In this case the person starts at the center of the rotating merry-go-round, and so I think we are to say their moment of inertia is zero or negligible (it would be small), but then they move to the outside edge of the merry-go-round, and in the after picture, have a significant moment of inertia. The moment of inertia of the merry-go-round is the same before and after and given as 670 kgm2