Recently, I was doing my homework and I found out that Angular Velocity and Angular Frequency can be calculated using $\omega=v/r$. This means the units of angular velocity and angular frequency are (meter/second)/meter or 1/second. Rotational frequency is also measured in $1/s$ which in Hz.

However, angular frequency is different from ordinary frequency. I am really confused as why it isn't measured in Hertz.

  • 1
    $\begingroup$ Are you confused as to why it is measured in Hertz or why it isn't measured in Hertz? I am confused because your sentence "angular frequency is different from ordinary frequency" seems to suggest that you would be happy if it were not measured in Hertz. But your title of the question (as well as the sentence "I am really confused why it isn't measured in Hertz") seems to suggest otherwise. $\endgroup$ – Dvij D.C. Mar 19 '19 at 2:06
  • $\begingroup$ Rotational velocity is measured in radians per second which is different from Hertz although they occupy the same dimension space. $\endgroup$ – John Alexiou Mar 19 '19 at 2:17
  • $\begingroup$ The standard units of torque by the way is Newton-meters, and is the rotational equivalent of Force. Is that a typo or does this need clarification? $\endgroup$ – Ryan Franz Mar 19 '19 at 21:42

The intended meaning of the hertz unit is that one hertz represents one complete occurrence of a cyclic phenomenon in one second. Angular frequency is not the number of complete rotations occurring per unit time, but instead the angle covered over that unit of time. Technically, angular frequency is not measured in


but instead in


that is, radians per second, so angle turned through per unit time. However, because the radian is defined as dimensionless, these two are mathematically equivalent. Conceptually, however, they are very different.

The correct quantity to measure in hertz when concerning rotational motion is ordinary frequency:

$$f = \frac{\omega}{2\pi\ \mathrm{rad}}$$

where the unit has been added for clarity, and this is the number of full rotations per second, thus suitable to measure with Hertz. More commonly, though, we use the non-metric unit revolutions per minute (RPM). One RPM is equal to $\frac{1}{60}\ \mathrm{Hz}$ or about $17\ \mathrm{mHz}$, and conversely, 1 Hz equals 60 RPM.


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