A uniform disk with mass m = 8.57 kg and radius R = 1.36 m lies in the x-y plane

Question

A uniform disk with mass m = 8.57 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 338 N at the edge of the disk on the +x-axis, 2) a force 338 N at the edge of the disk on the y-axis, and 3) a force 338 N acts at the edge of the disk at an angle ? = 31 above the x-axis.

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

N-m

2)

What is the magnitude of the torque on the disk about the z axis due to F2?
N-m

3)

What is the magnitude of the torque on the disk about the z axis due to F3?
N-m

4)

What is the x-component of the net torque about the z axis on the disk?
N-m

5)

What is the y-component of the net torque about the z axis on the disk?
N-m

6)

What is the z-component of the net torque about the z axis on the disk?
N-m

7)

What is the magnitude of the angular acceleration about the z axis of the disk?
rad/s2

8)

If the disk starts from rest, what is the rotational energy of the disk after the forces have been applied for t = 1.6 s?
J

A uniform disk with mass m = 8.57 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 338 N at the edge of the disk on the +x-axis, 2) a force 338 N at the edge of the disk on the a??y-axis, and 3) a force 338 N acts at the edge of the disk at an angle ? = 31A above the a??x-axis. What is the magnitude of the torque on the disk about the z axis due to F1? N-m 2)What is the magnitude of the torque on the disk about the z axis due to F2? N-m 3)What is the magnitude of the torque on the disk about the z axis due to F3? N-m 4)What is the x-component of the net torque about the z axis on the disk? N-m 5)What is the y-component of the net torque about the z axis on the disk? N-m 6)What is the z-component of the net torque about the z axis on the disk? N-m 7)What is the magnitude of the angular acceleration about the z axis of the disk? rad/s^2 8)If the disk starts from rest, what is the rotational energy of the disk after the forces have been applied for t = 1.6 s? J

Explanation / Answer

Torque = Force * Perpendicular Disdtance

(1)

Magnitude of Torque due to F1 =
= F1 * R
= 338 * 1.36
= 459.68 Nm

Diretion - Anticlockwise

(2)

Magnitude of Torque due to F2 = 0

(3)

Magnitude of Torque due to F3 =

= F3 * R * cos(31)
= 338 * 1.36 * cos(31)
= 394.02 Nm

Diretion - Clockwise

(4)
x-component of the net torque about the z axis on the disk = 0

(5)
Y-component of the net torque about the z axis on the disk = 0

(6)
z-component of the net torque about the z axis on the disk = 459.68 - 394.02 Nm

z-component of the net torque about the z axis on the disk = 65.66 Nm

(7)
Torque = Moment of Inertia * Angular Acceleration
= I*

Moment of Inertia of Disk = 1/2 * M*R^2
I = 1/2 * 8.57 * 1.36^2
I = 7.93 kG m^2

= /I
= 65.66 / 7.93
= 8.28 rad/s2
Angular acceleration about the z axis of the disk, = 8.28 rad/s2

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