Question

A uniform disk with mass m 8.64 kg and radius R 1.38 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 349 N at the edge of the disk on the +x-axis, 2) a force 349 N at the edge of the disk on the -y- axis, and 3) a force 349 N acts at the edge of the disk at an angle ? = 34° above the-x-axis. +X 2

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

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

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

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

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

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

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

h) 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?

Answer 1

As per Chegg guidelines, we are supposed to one question with maximum four subparts. I am doing it accordingly.

(a) Torque due to $F_1$ will be

$\tau_1=F_1r\sin90=349\times1.38\times1=481.62$ N-m$$

(b)

Torque due to $F_2$ will be

$\tau_2=F_2\times 0=0$

(c)

Torque due to $F_3$ will be

$\tau_3=F_3r\sin(-34)=-349\times1.38\times\sin34=-269.3185$ N-m$$

(d) There is no x-component of torque because torque is the cross product of position vector and force and it will be perpendicular to the plane (here XY plane) containing the two vector.

(e)  There is no y-component of torque because torque is the cross product of position vector and force and it will be perpendicular to the plane (here XY plane) containing the two vector.