A small, solid cylinder with mass 2 kg and radius 3 cm starts from rest and rota

Question

A small, solid cylinder with mass 2 kg and radius 3 cm starts from rest and rotates without friction about an axis through its center of mass. The rotation axis is fixed so that the center of mass of the cylinder does not move as the cylinder rotates. A string is wrapped around the circumference of the cylinder and is pulled using a constant force F=4 N.

1)

Which of the following statements is true?

2)

The cylinder will undergo

3)

4)

5)

6)

What is the angular velocity, ?, of the cylinder after the force has been pulling for 6 seconds?

7)

What is the magnitude of the work done by the string on the cylinder during the first 6 seconds?

8)

If we started at rest and pulled with the same force for twice the time, the how would its final angular velocity compare to the angular velocity in the previous situation?

Explanation / Answer

1. There is a non-zero net torque on the cylinder, but the net force on the cylinder is zero

2. angular acceleration but not linear acceleration.

3. I =mr^2 /2 = 2 x 0.03^2 /2 = 9 x 10-4 kg.m^2

4. torque = r x F = 0.03 x 4 = 0.12 N.m

5. torque = I x alpha
0.12 = 9 x 10-4 x lpha
alpha = 133.33 rad/s2

6. w = wi + alpha x t   = 0 + 133.33 x 6 = 800 rad/s

7. work done = Iw^2 /2   = 9 x10-4 x 800^2 /2 = 288 J

8. w = alpha xt
t new = 2 t
wnew = 2w

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