What is the difference between angular speed and tangential speed in a circular motion?

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 1/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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I know this is an old thread, but I had to figure this out for a problem on my physics homework.

What helped me to understand this is to think about 2 objects on a spinning disk, one being close to the center of the disk and one being close to the outside of the disk. Angular (rotation) speed deals strictly with the angle. How long does each object take to move an angle of pi when the disk is spinning? It takes them the same amount of time, so they have the same angular speed.

However, think about the actual speed of each object. The one that is further away from the center has to go a further distance to go around the circle than the one close to the center in the same amount of time, so it is going faster (tangential speed). For this reason the radius (how far it is from the center) must be considered in the tangential speed:

V_tangential = V_angular * radius


And simularly you can take the known tangential speed to find the angular speed:

V_angular = V_tangential / radius

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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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protected by Qmechanic♦Jul 3 '15 at 13:00

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