Circular motion

In classical mechanics, circular motion describes a broad class of problems. Notably, these problems are able to link the use of n-t coordinates and polar coordinates.

We have the following kinematic formulas:

$$v=r\dot{\theta }$$ $$a_n=\frac{v^2}{r}=r{\dot{\theta }}^2=v\dot{\theta }$$ $$a_t=\dot{v}=r\ddot{\theta }$$

We define the centripetal force as the force pointing towards $O$, i.e.,

$${\vec{F}}_n=m{\vec{a}}_n=\frac{m{v}^2}{r}$$