You are to design a rotating cylindrical axle to lift 800 {\rm N} buckets of cement from the ground to a rooftop 78.0 {\rm m} above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise.

What should the diameter of the axle be in order to raise the buckets at a steady 2.00 {\rm cm/s} when it is turning at 7.5 {\rm rpm}?

If instead the axle must give the buckets an upward acceleration of 0.400 \,{\rm m}/{\rm s}^{2}, what should the angular acceleration of the axle be?

Question

You are to design a rotating cylindrical axle to lift 800 {\rm N} buckets of cement from the ground to a rooftop 78.0 {\rm m} above the ground. The buckets will be attached to a hook on the free end of a cable that wraps around the rim of the axle; as the axle turns, the buckets will rise.


What should the diameter of the axle be in order to raise the buckets at a steady 2.00 {\rm cm/s} when it is turning at 7.5 {\rm rpm}?


If instead the axle must give the buckets an upward acceleration of 0.400 \,{\rm m}/{\rm s}^{2}, what should the angular acceleration of the axle be?