Why Are Radians Used in Calculating Tangential Speed?

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Tangential speed is calculated using the formula Vt = rω, where r is the radius in meters and ω is the angular velocity in radians per second. The resulting unit of tangential speed is indeed meters per second, as radians are dimensionless and effectively cancel out in the calculation. The discussion highlights the importance of using radians for angular measurements because they provide a direct relationship between linear and angular quantities. The question of why meters per radian per second is not used stems from the fact that radians do not have a physical dimension, simplifying the calculation. Understanding these concepts is crucial for accurate calculations in physics and engineering.
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Just calculated the Tangential speed that music is detected from a CD. I found it using Vt=r\omega where r was in meters and \omega I converted from revolutions per second to radians per second.

What unit of measure is tangential speed in?

Thanks,
Leah
 
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I'm guessing it's meters per second, but where do the radians go? And why do we not use meters per radian per second?

Just delving too far into this tonight...
 

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