A uniform disk with mass m = 8.98 kg and radius R = 1.33 m lies in the x-y plane and centered at the origin. Three forces act in the +y-direction on the disk:

1) a force 300 N at the edge of the disk on the +x-axis,

2) a force 300 N at the edge of the disk on the -y-axis, and

3) a force 300 N acts at the edge of the disk at an angle θ = 37^o above the -x-axis.

1) What is the magnitude of the torque on the disk about the z axis due to F₁? 

2) What is the magnitude of the torque on the disk about the z axis due to F₂? 

3) What is the magnitude of the torque on the disk about the z axis due to F₃? 

4) What is the x-component of the net torque about the z axis on the disk?

5) What is the y-component of the net torque about the z axis on the disk?

6) What is the z-component of the net torque about the z axis on the disk?

7) What is the magnitude of the angular acceleration about the z axis of the disk?

8) If the disk starts from rest, what is the rotational energy of the disk after the forces have been applied for t = 1.7 s?