# In circular motion, What does it mean s = r.θ?

In the circular motion, What does it mean by this equation s = r.θ?

S=rø is the formula for arc length, or angular displacement (ø rad).

Ø is the angle measure in radians.

Delta2
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The scheme is not perfect but I think you get the idea...

If you want to know how this equation is proved:

Due to symmetry of the circle we can assume that the arc length ##s## will be directly proportional to the angle ##\theta##. So it will be

##s=k\theta## (1) for some constant k.

But we know for angle ##2\pi## corresponds arc length ##2\pi r##. So if we apply equation (1) for those pair of data we get

##2\pi r=k (2\pi)## from which we can deduce that the constant k is actually the radius of the circle, ##k=r##.

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Dale