(9) [7 points] A child of mass M stands on a playground merry-go-round1 that is at rest. The moment of inertia ofthe merry-go-round is I and has radius R. The child stands partway to the edge of the merry-go-round from the center (you may take them as a point mass for estimation). The child throws a block of mass m at speed 17 at an angle of 6 as defined in the diagram. Assume frictionless rotation of the merry-go-round. (3) Use conservation of angular momentum to find an expression for the time it takes the merry- go-round to make one revolution. (b) Calculate the rotation period using I = 80 kg m2, M = 35 kg, 1' = 1.2 m, m = 1.2 kg, 1) = 4.0 m/s, and 9 = 30. OPTIONAL: no extra points, just extra thinking for personal satisfaction: (c) The child is disappointed with how fast the merry-go-round is spinning. They can't throw the block any faster. What changes do you recommend for the child to get maximum rotational enjoyment