How do you convert meters per second to RPM's?

You need more information to specify exactly what you are trying to do here, but I can give you one common example that will hopefully get you on the right track.

If you take the example of a cylinder spinning about it's axis, then you can convert between its rotational speed in revolutions per minute (RPM) and the tangential surface velocity (m/s) if you know the diameter of the cylinder. Essentially, you divide the time of one rotation into the circumference of the cylinder.

Legend:

V = tangential surface velocity

C = circumference of cylinder

D = diameter of cylinder

RPM = revolutions per minute

Pi = 3.14

Equations:

V = C * RPM = Pi * D * RPM

or

RPM = V / (Pi * D)

Example:

A cylinder with a diameter of 1 meter is rotating at 60 rpm. Its tangential surface velocity is:

V = (3.14) * (1 m) * (60 rpm) = 188.4 m/min = 3.14 m/s.