The pulley shown above, with radius 0.6 m and mass 5.5 kg, has a rope wrapped ar
ID: 1517458 • Letter: T
Question
The pulley shown above, with radius 0.6 m and mass 5.5 kg, has a rope wrapped around it. If one end of the rope is pulled with a constant force 5 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
torque = F * R
and = I* = ½MR²*
so angular acceleration
= 2FR / MR² = 2F / MR
= 2 * 5N / 5.5kg*0.6m = 3.03 rad/s²
² = ² + 2
² = 0² + 2 * 3.03rad/s² * 3*2 = 114.24 rad²/s²
= 10.688 rad/s
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