A uniform disk with mass m = 9.09 kg and radius R = 1.37 m lies in the x-y plane

Question

A uniform disk with mass m = 9.09 kg and radius R = 1.37 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 316 N at the edge of the disk on the +x-axis, 2) a force 316 N at the edge of the disk on the A uniform disk with mass m = 9.09 kg and radius R = 1.37 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 316 N at the edge of the disk on the +x-axis, 2) a force 316 N at the edge of the disk on the

Explanation / Answer

1)

T1 = F1*r = 316*1.37 = 432.92 Nm

2)

T2 = 0 (since force is aligned with origin)

3)

T3 = 0 (since force is aligned with origin)

4)

x-component of net torque about z-axis = 0

5)

y-component of net torque about z-axis = 0

6)

z-component of net torque about z-axis = 432.92 Nm

7)

Angular acceleration = Torque / Inertia

Inertia of disk = 1/2*mr^2 = 1/2*9.09*1.37^2 = 8.53 kg-m^2

Angular acceleration = 432.92 / 8.53 = 50.75 rad/s^2

8)

After 1.5 s, angular velocity = 1.5*50.75 = 76.124 rad/s

Kinetic energy = 1/2*Iw^2

= 1/2 *8.53*76.124^2

= 24715.35 J

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