# Pure Rotation

### Rotation about a fixed axis

Pure rotation occurs when a body rotates about a fixed non-moving axis. The following figure illustrates fixed-axis rotation.

### Motion characteristics

**Angular position:**(θ) Angular position relative to an inertial coordinate axis. Similar to how θ was measured in polar coordinates.**Angular velocity:**(ω) How fast a body is rotating.**Angular acceleration:**(α) How fast a body's rotation rate is increasing or decreasing.

### Angular kinematic relationships

**Angular velocity:**The time rate of change of angular position. ω = dθ/dt**Angular acceleration:**The time rate of change of angular acceleration. α = dω/dt = d^{2}θ/dt^{2}**Angular velocity / Angular acceleration:**Combining the angular velocity and acceleration equations, we obtain α dθ = ω dω.

### Angular motion parameter units

### Angular motion direction

#### If the rigid body, shown in the above figure, is rotating in the counterclockwise direction, what direction is its angular velocity?