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During Uniform Circular Motion, the linear speed of the particle is defined as the radius times the angular speed. $$ v = r\omega $$ The units of linear speed is meters/second (m/s). But the units of $ r\omega $ is $ m\frac {rad}{s} $. How is this possible? And why does the unit "radian" cancel out?

Qmechanic
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Vinay
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1 Answers1

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Rad is a dimensionless unit. It is defined as such an angle that it intercepts an arc on a circle with the length equal to the radius of a circle. Angle in radians is the length of an arc over radius, therefore meter over meter: $\theta = L_{arc}/R$. They are dimensionless in nature and people write "rad" simply for convenience.

Andrei Z.
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