Simply by using our intuition, we can begin to see the interrelatedness of rotational quantities like* θ* (angle of rotation), *ω* (angular velocity) and *α* (angular acceleration). For example, if a motorcycle wheel has a large angular acceleration for a fairly long time, it ends up spinning rapidly and rotating through many revolutions. The wheel's rotational motion is analogous to the fact that the motorcycle's large translational acceleration produces a large final velocity, and the distance traveled will also be large.

## Kinematic Equations

Kinematics is the description of motion. We have already studied kinematic equations governing linear motion under constant acceleration:

Similarly, the kinematics of rotational motion describes the relationships among rotation angle, angular velocity, angular acceleration, and time. Let us start by finding an equation relating *ω*, *α*, and *t*. To determine this equation, we use the corresponding equation for linear motion:

As in linear kinematics where we assumed *a* is constant, here we assume that angular acceleration *α* is a constant, and can use the relation:

By using the relationships *a=rα*, *v=rω*, and *x=rθ*, we derive all the other kinematic equations for rotational motion under constant acceleration:

The equations given above can be used to solve any rotational or translational kinematics problem in which a and α are constant. shows the relationship between some of the quantities discussed in this atom.

## Linear and Angular

This figure shows uniform circular motion and some of its defined quantities.