Rigid Body Mechanics/Torque

Angular Displacement

One revolution = $360\deg$ = $2\pi$ $rad$

Because how radians are just ratios of the circumference of a circle, you can write the arc length of the circle as

$s = r \theta$

where s is the arc length and r is the radius

Angular Velocity

Written as $\omega$

Angular displacement over time

This is not a measure of meters per second, as that is the tangential velocity

You can calculate tangential velocity with $\omega \cdot r$

Angular Acceleration

The rate of change of the angular velocity, measured in $rad$ $s^{-2}$

Kinematic Formulas

You can use all of the linear kinematic equations with angular

$\Delta\theta = \frac{\omega_f + \omega_i}{2} + t$

$\omega_f = \omega_i + \alpha t$

$\Delta\theta = \omega_it+\frac{1}{2}\alpha t^2$

$\omega_f^2 = \omega_i^2 + 2 \alpha \Delta \theta$

Center of Mass

The center of where all the mass is concentrated

Center of Gravity

The center of the force of gravity

Moment of Inertia

The measure of angular inertia or the resistance to change

The moment of inertia for a single point is $I = mr^2$

The moment of inertia for a system is $I = \sum_i m_ir_i^2$