A piece of 'chalk' is going around a fixed axis 00' as shown in figure. The chalk does not rotate about its own axis in any fashion. What can be said about this motion of the chalk piece?
Pure Translation
You may notice that
Any random point on the chalk piece do not follow circular path around 00'. As an example- take a print which is initially at r1 away from 00'. What do you think?
Now, you should also notice that at any instant, the velocities or to be more precise instantaneous velocities of all point of the body have equal magnitude as well as direction.
Also the body is always parallel to itself. This can be demonstrated by sketching any straightline on the body and comparing it all instants throughout its motion.
Hence this motion is purely translation.