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? rad/s (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? rad/s

Explanation / Answer

Using law of conservation of angular momentum

angular momentum before collision = angular momentum after the collision

I1*w1 = I2*w2

[(0.5*3M*R^2)+(M*(R/2)^2)]*3 = [(0.5*3M*R^2)+(M*R^2)]*w2

1.75*M*R^2*3 = 2.5*M*R^2*w2

1.75*3 = 2.5*w2

w2 = (1.75*3)/2.5 =2.1 rad/s

b) using law of conservation of angular momentum

[(0.5*3M*R^2)+(M*(R/2)^2)]*3 = 0 + (M*R^2)*w

1.75*M*R^2*3 = M*R^2*w

1.75*3 = w

w = 5.25 rad/s

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