Question

Question #6ae2f

Answer 1

Angular velocity has units of per second, angular frequency has units of per second, so we consider them the same thing.

Explanation:

The reason that this works is because radians are a unitless ratio.

`\theta = s/r`

Where `\theta` is an angle in radians, `s` is an arc length (in units of length, like meters) and r is the radius of your circle (in units of length, like meters).

Dividing, for example, meters over meters cancels, leaving you unitless. We usually say an angle is measured in radians to make it clear that we don't mean degrees, but it is not a real unit like a meter or a gram.

Angular velocity is the number of radians you cover per unit time:
`\omega = \theta / t`

and the units are:

`{rad}/ t` or since radians are unitless `1 / t`

Angular velocity has units of per second and so does angular frequency, so physicists consider them the same thing. I agree that this is a confusing convention.