# Curvilinear abscissa = radius * angle - Circular motion

I would like to understand why:

$$s(t) = r \, \theta(t)$$

where $$s$$ is the curvilinear abscissa, $$r$$ the radius and $$\theta$$ the angle in circular motion.

• It is just how the planar angle $\theta$ is defined and measured. It is the ratio of the arc-length to the radius of a circle. – Shubham Johri Jan 9 at 10:05