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.

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?

5.09 cm

Explanation:

using the formula

V = rω where r is radius and ω is the angular speed and V is the speed

ω = 7. 5 rpm = 7.5 × 2πrad / 60 seconds = 0.7855 rad s⁻¹ since one revolution = 2π and 1 minutes = 60 seconds

2.00 cm/s =r ×0.7855 rad s⁻¹

r = 2.00 cm/s / 0.7855 rad s⁻¹ = 2.546 cm

d = 2r =2 × 2.546 cm = 5.09 cm

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