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I was looking a long time for the way the equations of this two speeds are obtained, and i found pretty much nothing important, so can someone explain how are those obtained, and which is the difference between them?

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angular speed is the rate of change of the angle (in radians) with time, and it has units radians/s, while tangential speed is the speed of a point on the surface of the spinning object, which is the angular speed times the distance from the point to the axis of rotation.

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Symbolically,

$$[\omega] = s^{-1}$$ $$\omega = \frac{v}{r}$$

where $\omega $ is angular velocity, $v$ is tangential velocity and $r$ is distance between the moving particle and axis of rotation.

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