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What are the measurement units of $\omega$ in this equation and why

$$Y(x,t)=\,A\cos(kx-\omega t)?$$

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2 Answers

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It is radians per second, so when you multiply $\omega$ by $t$, $\omega t$ has units if radians.

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$ \ \omega \ $ is called "angular frequency" in physics and engineering, and has units of radians/second. Since radian is a "dimensionless unit" (because angle is defined as the ratio of arclength along a circle to the radius of said circle), the radian unit is often not written.

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