Physics
posted by Charlie .
A merrygoround with r = 4m and a perfect frictionless bearing is pushed with a force of 24 N by a young girl. She pushes with a constant force that is oriented tangentially to the edge of the merrygoround. After she pushes the merrygoround through 14 full rotations (at which point she lets go) it is spinning with an angular speed of 3 rad/s.
a. What is the moment of inertia of the merrygoround?
b. After the girl lets go, a 20 kg boy jumps onto the merrygoround and sticks halfway between the center of the edge. How fast are the merrygoround and the boy spinning after he lands?

ah, it turns out I took this course in 1955 and have had lots of practice since. I do not need to do your homework. However you do. Try the problems then comeback to us with specific things you are stuck on.
The first part is moment or torque = moment of inertia * angular acceleration, alpha
with constant alpha:
omega = omega initial + alpha * t
angle = initial angle + omega initial*t + (1/2) alpha * t^2
The second part is conservation of angular momentum with the moment of inertia increased by the mass of the boy times the square of distance from center. 
By the way to find the time it is easy to use the average velocity (3/2 = 1.5 radians/sec) for 14 *2 pi radians