International System of Units
According to the International System of Units (SI), rpm is not a unit. This is because the Revolution is a semantic annotation rather than a unit. The annotation is instead done in the subscript of the formula sign if needed. Because of the measured physical quantity, the formula sign has to be f for (rotational) frequency and ω or Ω for angular velocity. The corresponding basic SI unit is s−1 or Hz. When measuring angular speed, rad·s−1 can also be used as unit.
1 rad·s−1 = 60/2π rpm = c.9.55 rpm = 1/2π Hz.
Even though angular velocity, angular frequency and hertz all have the dimensions of 1/s, angular velocity and angular frequency are not expressed in hertz, but rather in an appropriate angular unit such as radians per second. Thus a disc rotating at 60 revolutions per minute (rpm) is said to be rotating at either 2π rad/s or 1 Hz, where the former measures the angular velocity and latter reflects the number of complete revolutions per second. The conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second are:
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