We will focus on rotation about a single axis of rotation, which is analogous to one-dimensional straight-line motion. Basically, if you understand 1-D motion you can do rotation - rotational motion is really just straight-line motion rolled up into a circle.

Displacement, velocity, and acceleration all have rotational equivalents. There are also rotational equivalents of mass, force, Newton's Laws, kinetic energy, momentum, etc. Any equation we used for straight-line motion has a rotational form that can be found by substituting the equivalent rotational variables.

For instance, how are angles, angular velocities, and angular accelerations related? The same way the linear variables are:

Angular velocity is the rate of change of angle

Instantaneous angular velocity:

ω

=

dθ dt

Average angular velocity:   ωavg

=

Δθ Δt

Angular acceleration is the rate of change of angular velocity

Instantaneous angular acceleration:

α

=

dω dt

Average angular acceleration:   αavg

=

Δω Δt