Question

Pulleys and Belts
In a pulley system, pulley A is moving at 1500 rpm and has a diameter of 15 in. Three pulleys, B, C, and D, all of different sizes, are attached to a single output axle. Speed and torque output are changed within the system by moving the drive belt between pulleys B, C, and D.
1.A speed of 1750 rpm is required when the drive belt is connected to pulley B. What is the diameter of pulley B?
2.A speed of 2000 rpm is required when the drive belt is connected to pulley C. What is the diameter of pulley C?
3.A speed of 3250 rpm is required when the drive belt is connected to?

Answer 1

for this question I would use the similarities between pulley A, to each pulley of the question.
like this for question 1...
\[\frac{ 15 inches }{ 1500 rpm} = \frac{ ? inches }{ 1750 rpm}\]

so, isolating the unknown
\[\frac{ 15inches * 1750rpm }{ 1500 rpm} = ? inches = 17.5 inches for the diameter\]

I know this idea seems to simple, but it is correct so long as nothing else changes. or that we have 3 knowns and 1 unknown.