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

1. Aug 9, 2018

### HCverma

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

2. Aug 9, 2018

### Luke Velie

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

Ø is the angle measure in radians.

3. Aug 9, 2018

### Delta²

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, $k=r$.

Last edited: Aug 9, 2018