Circular motion is the movement whose trajectory describes a circular arc.
All units are in the International System (\(IS\)).
We can relate this movement to a linear motion: \( s(t) = r\phi(t)\), \( v(t) = r\omega(t)\) and \( a(t) = r\alpha(t)\).
Time related functions in uniform circular motion: \begin{align} \omega(t) &= \omega_0 \notag \\ \phi(t) &= \phi_0 + \omega_0 t \notag \end{align}
To describe a uniform circular motion, these quantities are also used:
Period and frequency relation: \( \tau = \frac{1}{f}\).
The angular velocity relation: \( \omega = \frac{2 \pi}{\tau} = 2 \pi f\).
It is the movement in which the angular acceleration is constant and different from zero. Its equations are analogous to the ones on the uniformly accelerated motion: \begin{align} \phi(t) &= \phi_0 + \omega_0 t + \alpha \frac{t^2}{2} \notag \\ \omega(t) &= \omega_0 + \alpha t \notag \\ \omega^2 &= \omega_0^2 +2 \alpha \Delta \phi \notag \end{align}