A metal disk with a radius of 10cm and a mass of 6 kg has a hole in the center a

Question

A metal disk with a radius of 10cm and a mass of 6 kg has a hole in the center and is nailed to a wooden post. The disk is free to rotate without friction. Two small lightweight rockets are glued to opposite sides of the disk. The disk is initially at rest. Then the rockets are fired and the disk is made to rotate by the rockets, which each exert a force of 8N.

a) What is the moment of inertia of the disk?

b) What is the torque created by one of the rockets on the disk?

c) What is the total torque created by both rockets on the disk?

d) What is the angular acceleration of the disk?

e) What is the total distance traveled by one of the rockets during the first two seconds of rotation?

Explanation / Answer

a) Moment of inertia =1/2* Mr^2 = 0.03 kg-m^2

b)torque due to one rocket = F*r = 0.8 Nm

c) torque created by both rockets = 2*0.8 = 1.6 Nm

d)Angular acceleration = Torque / Moment of inertia = 1.6 / 0.03 = 53.34 rad/s^2

e) distance travelled, theta = ut + 1/2*(alpha)t^2 = 0 + 1/2*53.34*(2)^2 = 106.67 rad

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