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Revolutions per minute to Radians per second

Revolutions per minute to Radians per second
by Denny Flynn on 09/20/05 at 09:51:55

I was unable to find a conversion for RPM to radians per second.

Re: Revolutions per minute to Radians per second
by Wilfred on 10/07/05 at 20:46:52

"RPM conversion to radians per second"

The important thing here is to understand what a "radian" is.  It is usually thought of as an angular measure, namely 57.296 degrees (to three decimal places).

Where did this angular measure come from?
Remember the formula for the circumference of a circle:
C = 2 Pi * R
where C is the circumference, R is the radius, and Pi is a constant, with a value of 3.14159

A simple way to explain this is to think of an ant walking (running?) along the curve of a circle which you have just drawn on a sheet of paper.  Suppose that you have marked a spot on the circumference of your circle.  Suppose too that you have a very agreeable ant, and you ask the ant to walk around the circumference line.  When the ant has walked a distance exactly the same as the radius of the circle, he has walked a distance of one radian.

So to get back to RPM and radians per second.

Sixty RPM is 60 revolutions per minute, or one circumference per second, or (2 Pi) radians per second.

(2 Pi) radians per second is (2 * 3.14159) = 6.28318 radians per second, or
(2 * 3.14159 * 60) = 376.99 radians per minute (let's be bold and call it approx 377 radians per minute).

So we have 60 RPM = 6.28318 radians per second,
and 3600 RPM = 377 radians per second.

From this we can work out simple conversion factors:

1000 RPM = 104.72 radians per second (approx), and

1000 radians per second = 9,549 RPM (approx)

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