A particularly large playground merry-go-round is essentially a uniform solid di

Question

A particularly large playground merry-go-round is essentially a uniform solid disk of mass 3M and radius R that can rotate with no friction about a central axis. You, with a mass M, are a distance of R/2 from the center of the merry-go-round, rotating together with it at an angular velocity of 3.00 rad/s clockwise (when viewed from above). You then move to the outside of the merry-go-round so you are a distance R from the center, still rotating with the merry-go-round. Consider you and the merry-go-round to be one system.

(a) When you reach the outer edge of the merry-go-round, what is the angular velocity of the you and merry-go-round system?

(b) You then start running around the outer edge of the merry-go-round. At what angular speed would you have to run to make the merry-go-round alone come to a complete stop?

Explanation / Answer

(a) angular momentum conservation

Id wo + Im wo = Id w + Im w

wo ((3MR^2 / 2) + (MR^2 / 4) = w ((3MR^2 / 2) + (MR^2))

3 (7/4 MR^2) = w (5/2 MR^2)

w = 2.1 rad / s

(b) With the same angular speed as the marry go round rotates w = 2.1 rad/s

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