A uniform disk with mass m = 8.89 kg and radius R = 1.36 m lies in the x-y plane

Question

A uniform disk with mass m = 8.89 kg and radius R = 1.36 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 302 N at the edge of the disk on the +x-axis, 2) a force 302 N at the edge of the disk on the ?y-axis, and 3) a force 302 N acts at the edge of the disk at an angle ? = 30? above the ?x-axis.

1.) What is the x-component of the net torque on the disk?

2.) What is the y-component of the net torque on the disk?

3.) What is the z-component of the net torque on the disk?

4.) What is the magnitude of the angular acceleration of the disk?

5.) If the disk starts from rest, what is the rotational energy of the disk after the forces have been applied for t = 1.8 s?

Explanation / Answer

x and y component of torque is zero
z component of torque =302*1.36+0-302*1.36*cos30 =55.03 Nm
55.03 =I

I =8.89*1.36^2/2

hence =6.69 rad/s^2

w=6.69*1.8 =12.05

energy =1/2 Iw^2 =596.89J

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