Math CentralQuandaries & Queries


Question from Jason, a student:

7 in. pulley traveling @ 175ft/sec. What is the rpm?

Hi Jason,

175 feet is 175 × 12 inches so the pulley is travelling at 175 × 12 inches per second. The pulley has a radius of 7 inches so what is its circumference? This is the length of 1 revolution. How many seconds does it take for the pulley to make 1 revolution? How many minutes does it take for the pulley to make 1 revolution? This number has the units of minutes per revolution so one over this number is the angular speed in revolutions per minute.

Write back if you need more help,


Hi Jason.

A "revolution" would be the length of the circumference of the pulley. Pulleys are usually measured by their diameter, so your pulley revolvesonce in 7π inches. Now you have a linear conversion. From ft/sec you can convert to rev/sec by dividing by the circumference. Then you can multiply by 60 to convert rps into rpm, since there are 60 seconds in a minute.

Hope this helps,
Stephen La Rocque

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