A child pushes tangentially on a small hand driven merry- go- round. She is able to accelerate it from rest to 20 rpm in 10 s. Modeling the merry go round as a uniform disk of radius 3.5 m and mass 800 kg, find the torque required to produce that acceleration. Neglect the frictional torque.

Answer 1

now use your text and try to do the problems
torque = rate of change of angular momentum
= change in I omega/ change in time

initial omega = 0
final omega = 20 *2 pi /60 radians/second

Your text has a table of moments of inertia of shapes certainly including a solid disk with axis through the center like a wheel.
This is the last one I will help with. You are not trying.