# Units: Custom-defined units possible?

Converting between revolutions per minute (RPM) and revolutions per second (RPS) is not straightforward for me in Mathematica.

I know that $1\; \text{RPM} = \frac{2\; \times\; \Pi\; \text{Radian}}{\text{Second}\; \times\; 60}$. To get RPS then, it is just a matter to remove the factor of $60$ in the denominator.

Taking a numerical example, I can convert say $500$ RPM to Hertz as follows:

$[\text{Convert}[\frac{500\; \times\; 2\; \times\; \Pi\; \text{Radian}}{\text{Second}\; \times\; 60}, \text{Hertz}],9]$

which gives me $52.3597776\; \text{Hertz}$

But now if I want to convert $500$ RPM to RPS, the following does not work as in the Convert command, the second argument has also numerical values in it:

$[\text{Convert}[\frac{500\; \times\; 2\; \times\; \Pi\; \text{Radian}}{\text{Second}\; \times\; 60}, \frac{2\; \times\; \Pi\; \text{Radian}}{\text{Second}}],9]$

which gives me as output: $\frac{52.3598776\; \text{Radian}}{\text{Second}}$ instead of the desired answer of about $8.33\:$ . The factor of $2\; \Pi$ is the troublemaker.

So how to do an appropriate conversion from RPM to RPS?

update:

I am using version 9.

Thank you.

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Which version of Mathematica are you using? –  Mr.Wizard Dec 18 '13 at 9:45
If You are using Mathematica 9 You can try UnitConvert[] function. I'm using ver. 7.0 so I can't check if it works in Your case. –  Wojciech Dec 18 '13 at 9:48
@Wojciech yes, N@UnitConvert[Quantity[500,"Revolutions"/"Minutes"], "Revolutions"/"Seconds"] does give the result 8.333... –  cormullion Dec 18 '13 at 11:28
That one was pretty straightforward, since it is in the documentation center :) –  Wojciech Dec 18 '13 at 11:49
As does UnitConvert[Quantity[500., "RPM"], "RPS"] –  bobthechemist Dec 18 '13 at 13:55