How Does Angular Velocity Relate to Radians and Hertz?

[tony873004]

velocity = 0.5 m/s
radius = 1 m

$$\omega = \frac{v}{r}$$

$$\omega = \frac{0.5 m/s}{1 m}$$

the meters cancel and I'm left with

$$\omega = 0.5 s$$

But $$\omega$$ is supposed to be expressed in radians/s

How do I get those output units with the given input units?

 

[AKG]

Why do you have "w = 0.5s" when your calculations suggest it should be "w = 0.5/s = 0.5 Hz"? Note that radians are dimensionless, so rad/s is equivalent to 1/s, or Hz.

 

[ehild]

Why do you have "w = 0.5s" when your calculations suggest it should be "w = 0.5/s = 0.5 Hz"? Note that radians are dimensionless, so rad/s is equivalent to 1/s, or Hz.

Hertz (Hz) is the unit of frequency, and the unit of angular velocity is rad/s. Both frequency and angular velocity have the dimension of 1/[time], so they can be written also as 1/s.

See http://physics.nist.gov/cuu/Units/units.html

ehild