Question

A uniform disk with mass m = 9.04 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 309 N at the edge of the disk on the +x-axis, 2) a force 309 N at the edge of the disk on the –y-axis, and 3) a force 309 N acts at the edge of the disk at an angle θ = 30° above the –x-axis.

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

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

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

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

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

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

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

8) 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

1) |τ1| = 309N * 1.35m = 417.15 N·m

2) 0 N·m because r x F is zero (as they are parallel).

3) |τ3| = 309N * 1.35m * cos(180-30)º = 361.3 N·m

4) 0 ("the x-component of the net torque about the z axis" is zero.)

5) Again for the same reason, 0.

6) net τ = (417.15 + 0 - 361.3)N·m = 55.9 N·m

7) net τ = I * α

I = ½mR² = ½ * 9.04kg * (1.35m)² = 8.24 kg·m²

plug in net τ from part 6 and solve for α:

55.9 N·m = 8.24kg·m² * α

α = 6.79 rad/s²

8) ω = α * t = 6.79rad/s² * 1.8s = 12.2 rad/s

KE = ½ * I * ω² = ½ * 8.24kg·m² * (12.2rad/s)² = 615 J

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