Help with a physics question?

Question

You are to design a rotating cylindrical axle to lift 800-N buckets of cement from the ground to a rooftop 78.0 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.

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

B) If instead the axle must give the buckets an upward acceleration of , what should the angular acceleration of the axle be?

I need some help with this question. What equations do I need to use? Thanks in advance for the help!

Answer 1

Linear or tangential velocity V is related to angular velocity w as
A) V=w R where R- radius of rotation
w= rpm x 2 pi /60
D=2R= 2V/w= 2 x2.00/ (7.5 x2 pi /60)
D=5.09 cm
B) if the acceleration upward is a then angular acceleration A is
A=a/R

This is it.
Have fun