Finding angular acceleration, magnitude of torque and moment of intertia?

Question

The radius of a park merry-go-round is 2.0 m. To start it rotating, you wrap a rope around it and pull with a force of 260 N for 17 s. During this time, the merry-go-round makes one complete rotation.

(a) Find the angular acceleration of the merry-go-round.

_____rad/s2

(b) What is the magnitude of the torque exerted by the rope on the merry-go-round?

_____N·m

(c) What is the moment of inertia of the merry-go-round?

_____kg·m2

Answer 1

R=2 m

φ=angle of rotation

α=angular acceleration

T=torque

J=moment of inertia

a) For 17s the merry-go-round makes one complete rotation ==> φ=2π rad

φ=0.5αt^2

α=2*φ/t^2

α=2*2π/17^2

α=4π/289 rad/s2

b) T=F*R

T=260*2=520 N·m

c) T=J*α

J=T/α

J=520/(4π/289)  

J=37570/π kg·m2