Finding pulley diameter with speed in rpm

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SUMMARY

The discussion centers on calculating the diameter of pulley C in a pulley system where pulley A operates at 1,500 rpm with a diameter of 15 inches, and pulley C needs to achieve a speed of 2,000 rpm. To find the diameter of pulley C, users are advised to apply the relationship between the diameters and rotational speeds of the pulleys. The relevant equation is derived from the formula: (Diameter A / Diameter C) = (Speed C / Speed A), allowing for the calculation of pulley C's diameter based on the known values.

PREREQUISITES
  • Understanding of pulley systems and their mechanics
  • Familiarity with rotational speed (rpm) calculations
  • Knowledge of basic algebra for solving equations
  • Access to relevant textbooks or notes on pulley dynamics
NEXT STEPS
  • Study the relationship between pulley diameters and speeds using the formula: (Diameter A / Diameter C) = (Speed C / Speed A)
  • Explore examples of pulley systems in mechanical engineering textbooks
  • Learn about torque transmission in pulley systems
  • Investigate the impact of pulley size on system efficiency and performance
USEFUL FOR

Mechanical engineering students, hobbyists working on pulley systems, and anyone involved in designing or analyzing mechanical systems that utilize pulleys for speed and torque adjustments.

Tambourine Man
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Homework Statement



[/B]
In a pulley system, pulley A is moving at 1,500 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.

A speed of 2,000 rpm is required when the drive belt is connected to pulley C. What is the diameter of pulley C?

The question is here, how do I find the diameter? I don't know the input or output speeds.

Homework Equations



upload_2016-11-25_17-43-17.png

The Attempt at a Solution



2500/1500

(not sure if this is right)
[/B]
 
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Tambourine Man said:
The question is here, how do I find the diameter? I don't know the input or output speeds.

You sure about that?...
... pulley A is moving at 1,500 rpm...

...A speed of 2,000 rpm is required...

Homework Equations



View attachment 109424

There's no equality so that's not an equation.
You're looking for an equation that relates the diameter of a pair of pulleys with their rotational speed, check your notes and/or textbook. You know both RPM's and one diameter so can solve for the single unknown; the second pulleys diameter.
 

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