Speed Pertaining to Circular Motion

1. Sep 20, 2013

Coop

Units for Speed Pertaining to Circular Motion

Hi,

So v=ω*r

Where v = velocity in m/s
ω = angular velocity in rad/s

But I am confused...the units don't match! What happens to the rad?

My textbook doesn't explain it, it simply does calculations like (56.5 rad/s)(0.030 m) = 1.7 m/s and the rad disappears. I have a feeling I am missing something obvious . Any help?

Thanks,
Coop

Last edited: Sep 20, 2013
2. Sep 20, 2013

D H

Staff Emeritus
The measure of an angle θ, in radians, is defined as the ratio of a circular arc subtending that angle θ to the radius of the circle. Angles thus have units of length per length. In other words, angle is a unitless quantity. Using radians makes the constant of proportionality one when computing arc length, or when computing speed along a circular path.

3. Sep 21, 2013

dauto

In other words, rads is not a unit. It's just a label.

4. Sep 21, 2013

Coop

Cool, thanks a lot guys, I wish my book explained that :p