A uniform disk with mail m = 8.78 kg and radius R = 1.42 m lies to the x-y plane

Question

A uniform disk with mail m = 8.78 kg and radius R = 1.42 m lies to the x-y plane and centered at the origin. Three forces act in the + y-direction on the disk: a force 319 N at the edge of the disk on the +x-axis, a force 319 N at the edge of the disk on the -y-axis, and a force 319 N acts at the edge of the disk at an angle theta = 39 degree above the -x-axis. What is the magnitude of the torque on the disk about the z axis due to F_1? What is the magnitude of the torque on the disk about the z axis due to F_2? What is the magnitude of the torque on the disk about the z axis due to F_3? What is the x-component of the net torque about the z axis on the disk? What is the y-component of the net torque about the z axis on the disk? What is the z-component of the net torque about the z axis on the disk? What is the magnitude of the angular acceleration about the z axis of the disk? 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? Below is some space to write notes on this problem

Explanation / Answer

here,

radius , r = 1.42 m

a)

F1 = 319 N

torque due to force 1 , T1 = F1 * r

T1 = 319 * 1.42 = 452.98 N.m

b)

F2 = 319 N

as the angle between force and radius is 0 degree

the torque due to F2 is zero

3)

F3 = 319 N

the torque due to F3 , T3 = - F3 * r * cos(39)

T3 = - 319 * 1.42 * cos(39)

T3 = - 352.03 N.m

4)

the x componet of the torque about the z axis is zero

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