A uniform disk with mass m = 8.5 kg and radius R = 1.34 m lies in the x-y plane

Question

A uniform disk with mass m = 8.5 kg and radius R = 1.34 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 328 N at the edge of the disk on the +x-axis, 2) a force 328 N at the edge of the disk on the –y-axis, and 3) a force 328 N acts at the edge of the disk at an angle = 38° above the –x-axis.

1)

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 = 1.5 s?

J

Explanation / Answer

1) T1 = R*F1*sin(90)

= 1.34*328

= 439.52 N.m

2) T2 = 0

3) T3 = R*F3*sin(90-38)

= 1.34*328*sin(52)

= 346.3 N.m

4) Tnetx = zero

5) Tnety = zero

6) Tnetz = T1 - T2

= 439.52 - 346.3

= 93.22 N.m

7) Moment of Inertia of disk, I = 0.5*M*r^2

= 0.5*8.5*1.34^2

= 7.63 kg.m^2

Apply, alfa = Tnetz/I

= 93.22/7.63

= 12.2 rad/s^2

8) w = wo + alfa*t

= 0 + 12.2*1.5

= 18.32 rad/s^2

so, KE = 0.5*I*w^2

= 0.5*7.63*18.32^2

= 1281 J

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