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

Above two figures shows the different motion of the same body.

Suppose $P$ is any point and its centre of mass is at $O$.

The trajectories of $\mathrm{O}$ are the translational trajectories $\mathrm{T} r_{1}$ and $\mathrm{T} r_{2}$ of the body. The positions $\mathrm{O}$ and $\mathrm{P}$ at three different instants of time are shown by $\mathrm{O}_{1}, \mathrm{O}_{2}, \mathrm{O}_{3}$ and $\mathrm{P}_{1}, \mathrm{P}_{2}, \mathrm{P}_{3}$ respectively in both the figures.

In figure $(a)$ it is seen that position does not changes at different position. Line like $OP$ have no orientation, the angle makes by $OP$ in horizontal remains same.

$\therefore \alpha_{1}=\alpha_{2}=\alpha_{3}$

Such motion is a pure translation.

In pure translation motion particles like $\mathrm{O}$ and $\mathrm{P}$ have same velocity at different position. In figure $(b)$ in case of combination of translation and rotation, the velocity of $\mathrm{O}$ and $\mathrm{P}$ differ. $\therefore \alpha_{1} \neq \alpha_{2} \neq \alpha_{3}$.

Such type of motion is the combination of pure translation and combination of translation motion.

Another illustration of such type of motion : Rolling motion of a cylinder is another illustration of this motion. Here the motion of rolling of cylinder on a slope about fixed axis the combination of rotation and translational motion.

If a motion of rigid body is not about any axis or not stationary it is pure translation or combination of translation and rotation motion.

If the motion of body is pivoted or stationary by any way then this motion is rotational motion. Rotational motion may be about stationary and variable axis.