A uniform disk with mass m = 8.54 kg and radius R = 1.35 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 334 N at the edge of the disk on the +x-axis, 2) a force 334 N at the edge of the disk on the –y-axis, and 3) a force 334 N acts at the edge of the disk at an angle θ = 30° above the –x-axis.

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 = 1.6 s?

A) τ_1 = 450.9 N.m

B) τ_2 = 0 N.m

C) τ_3 = 390.47 N.m

D) There is no x-component.

E) There is no y-component.

F) τ_z = 60.43 N.m

G) α = 7.765 rad/s²

H) K = 600.6J

Explanation:

A) τ_1 = F1•r1•sinθ1

τ_1 = 334 x 1.35 x sin90

τ_1 = 450.9 N.m

B) τ_2 = F2•r2•sinθ2

τ_2 = 334 x 1.35 x sin180

τ_2 = 0 N.m

C) τ_3 = F3•r3•sinθ3

τ_3 = 334 x 1.35 x sin60

τ_3 = 390.47 N.m

D) Torque from F2 is zero and both torques from F1 and F3 are in z direction, thus, there is no x-component.

E) Torque from F2 is zero and both torques from F1 and F3 are in z direction, thus, there is no y-component.

F) τ_1 is in the positive z direction

τ_2 is zero

τ_3 is in the negative z direction

Hence, τ_z = 450.9 - 390.47 = 60.43 N.m

G) moment of inertia is given as ;

I = (1/2)MR²

Thus ;

I = (1/2) x 8.54 x 1.35² = 7.782 N.m

Angular acceleration is;

α = τ_z/I

α = 60.43/7.782 = 7.765 rad/s²

H) angular velocity is;

ω = αt = 7.765 x 1.6 = 12.424 rad/s

Rotational energy, K = (1/2)Iω²

K = (1/2) x 7.782 x (12.424)² = 600.6J

the earths atmosphere is made up of nitrogen and oxygen. solids can turn into gasses through a process called sublimation. sublimation is the transition of a substance directly from the solid to the gas phase, without passing through the intermediate liquid phase.

hope this : d

jupiter is the largest planet in our solar system, having a mass and radius that are respectively, 318 and 11.2 times that of earth. suppose that an object falls from rest near the surface of each planet and that the acceleration due to gravity remains constant during the fall. each object falls the same distance before striking the ground. determine the ratio of the time of fall on jupiter to that on earth.