The pulley shown above, with radius 0.7 m and mass 4.0 kg, has a rope wrapped ar

Question

The pulley shown above, with radius 0.7 m and mass 4.0 kg, has a rope wrapped around it. If one end of the rope is pulled with a constant force 7 N, how fast is the pulley rotating after it has gone through 3 revolutions? Assume that the pulley is uniform, so its moment of inertia is 1/2 M R2, the rotation is frictionless, and the mass of the rope can be neglected. Give your answer in rad/sec to at least three significant figures. You will not be graded on the number of digits, this is just to avoid rounding errors.

Explanation / Answer

W = 1/2I^2 = T

1/2*1/2MR^2*^2 = T

1/4MR^2*^2 = T

1/2*4.0*0.7^2*^2 = 7.0*3*2*3.14

Simplifying, = 11.6 rad/s

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