Explain with illustration the pure translation and combination of translation and rotation motion of a rigid body.

(N/A) The provided figure illustrates two different types of motion for the same rigid body.
Suppose $P$ is any point on the body and its center of mass is at $O$.
The trajectories of $O$ are the translational trajectories $Tr_{1}$ and $Tr_{2}$ of the body. The positions of $O$ and $P$ at three different instants of time are shown by $(O_{1}, O_{2}, O_{3})$ and $(P_{1}, P_{2}, P_{3})$ respectively in both figures.
In figure $(a)$,it is observed that the orientation of the body does not change as it moves. The line segment $OP$ maintains a constant angle with the horizontal direction at all positions.
$\therefore \alpha_{1} = \alpha_{2} = \alpha_{3}$
Such motion is defined as pure translation.
In pure translational motion,all particles of the rigid body,such as $O$ and $P$,have the same velocity at any given instant. In figure $(b)$,which represents a combination of translation and rotation,the velocities of $O$ and $P$ differ because the body rotates as it translates. Consequently,$\alpha_{1} \neq \alpha_{2} \neq \alpha_{3}$.
This type of motion is a combination of pure translation and rotation.
Another illustration of such motion is the rolling motion of a cylinder. When a cylinder rolls down a slope,its motion is a combination of rotation about its central axis and the translational motion of its center of mass.
If the motion of a rigid body is not about a fixed axis or is not stationary,it is either pure translation or a combination of translation and rotation.
If the motion of a body is constrained to be about a fixed axis or is pivoted,it is classified as rotational motion. Rotational motion can occur about a stationary axis or a variable axis.