How Does Angular Velocity Relate to Radians and Hertz?

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SUMMARY

The discussion clarifies the relationship between angular velocity, radians, and Hertz using the formula ω = v/r, where v is linear velocity and r is radius. Given a linear velocity of 0.5 m/s and a radius of 1 m, the calculated angular velocity is 0.5 rad/s. The confusion arises from the equivalence of radians per second (rad/s) and Hertz (Hz), both of which represent frequency as 1/s. The discussion emphasizes that radians are dimensionless, confirming that ω = 0.5 rad/s is equivalent to 0.5 Hz.

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tony873004
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velocity = 0.5 m/s
radius = 1 m

[tex]\omega = \frac{v}{r}[/tex]

[tex]\omega = \frac{0.5 m/s}{1 m}[/tex]

the meters cancel and I'm left with

[tex]\omega = 0.5 s[/tex]

But [tex]\omega[/tex] is supposed to be expressed in radians/s

How do I get those output units with the given input units?
 
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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.
 
AKG said:
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
 

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