Question

03. A child of mass 30kg is sitting on the edge of a merry, in the shape of a solid disk of mass 200kg and radius 2m. The child and the merry-go-round rotate once every 3.14s. The child jumps off of the merry-go-round tangentially so that its velocity relative to the edge of the merry go round is 2m/s in the opposite direction to the rotation. a) Write down the formulae for the child and the merry-go-round explain any approximations made. (6 points) b) Calculate the total moment of inertia of the system numerically (3 points) c) Write down an expression for the initial angular velocity and calculate it. (6 points) d) Write down an expression for the linear velocity of the child and calculate it. (5 points) e) Write down an expression for the velocity of the child relative to the ground and use it to calculate the angular velocity of the child just after the jump. (4 points) f) Explain how to find the final angular velocity of the merry-go-round. Write down reasoning and a logical sequence of formulae to derive an expression for the final angular velocity of the merry-go-round and evaluate it numerically. (6 points)