Explain the definitions of angular position,angular displacement,and angular speed for the motion of a rigid body.

(N/A) $1$. Angular Position: The angular position of a particle in a rotating rigid body is defined by the angle $\theta$ it makes with a reference line (usually the $x$-axis) in the plane of rotation at any given time $t$.
$2$. Angular Displacement: When a particle moves from position $P$ to $P^{\prime}$ in a time interval $\Delta t$,the change in its angular position is called angular displacement,denoted by $\Delta \theta = \theta_2 - \theta_1$.
$3$. Angular Speed: The average angular speed $\langle \omega \rangle$ is defined as the ratio of angular displacement to the time interval,$\langle \omega \rangle = \frac{\Delta \theta}{\Delta t}$. The instantaneous angular speed is $\omega = \lim_{\Delta t \to 0} \frac{\Delta \theta}{\Delta t} = \frac{d\theta}{dt}$.
In the figure,a rigid body rotates about a fixed axis $Oz$. All particles move in circular paths perpendicular to this axis. For a particle at $P$ with radius $r$ and center $C$,the angular displacement in time $\Delta t$ is $\angle PCP^{\prime} = \Delta \theta$.