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 3.40 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. When you reach the outer edge of the merry-go-round, what is the angular velocity of the you and merry-go-round system? rad/s 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? rad/s

Explanation / Answer

(I1+I2)1=(I1+I3)2

(3MR^2+MR^2/4)1=(3MR^2+MR^2)2

3.251=42

2=2.76rad/s

now if u want to stop it

I12=I33

3=3*2.76=8.28rad/s in anti clockwise direction

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