# Physics concept help? ?

I'm having a lot of trouble with a study guide question from my rotation unit, please help!

1. A mery-go-round is a playground ride that consists of a large disk mounted to that it can freely rotate in a horizontal plane. The merry-go-round shown is initially at rest, has radius R=1.5 m, and a mass M=226kg. A small boy of mass m=49kg runs tangentially to the merry-go-round at a speed of v=1.1m/s, and jumps on.

a. calculate the moment of inertia of the merry-go-round, in kg*m^2

b. immediately before the boy jumps on the merry go round, calculate his angular speed (in rad/s) about the central axis of the merry go round.

c. immediately after the boy jumps on the merry go round, calculate the angular speed in radians/second of the merry go round and boy.

d. the boy then crawls towards the center of the merry go round along a radius. what is the angular speed in rad/s of the merry go round when the boy is half way between the edge and the center of the merry go round?

e. the boy then crawls to the center of the merry go round. what is the angular speed in radians/second of the merry go round when the boy is at the center of the merry go round?

f. finally, the boy decides that he has had enough fun. he decides to crawl to the outer edge of the merry go round and jump off. somehow, he manages to jump in such a way that he hits the ground with zero velocity with respect to the ground. what is the angular speed in radians/second of the merry go round after the boy jumps off?

Relevance
• a. Assuming a uniform disk, I = ½MR²

b. ω = v / R

c. conserve angular momentum

I_boy * ω = (I_disk + I_boy) * ω'

where ω' is the new angular velocity.

and I_boy = mR²

d. Now I_boy = m*(R/2)². Find new ω'.

e. Now I_boy = 0. Find new ω'.