If you were an ant on the string tied ball, which is orbiting a second larger object, (ball always presenting only one side to larger object of course) and smart enough to note in which direction the string was pointing out into space, then you would see that "sting extended point" in the heavens moving around large circle amoung the stars. Thus the string tied ball is rotating.
MORE GENERALLY:
Any motion of any ridged body can be considered to be composed of two distinct types of motion: Rotation and Translation.
A vector (or speed & direction if you are not familiar with vectors) is associated with both and these vectors can change with time, but at any given instant, their directions are uniquely defined.
EXAMPLE:
Translation part:
If you place yourself on the rigid object and have the normal egotistical attitude then you do not consider that you are translating. For example while sitting at your desk you actually have a very complex translation with the sun thru space (in essentially a constant direction and speed, neglecting the small wobble Jupitor makes in the sun's trajectory thru space) and you are also in near circular orbit about the sun, so this is the next major part of your translation motion but now the direction of this slower component is not constant. It is constantly and steadly changing (after one year it will start repeating). There is still a third and minor component of your total translation, due to fact your desk is not at the mass center of the Earth (actually the Earth moon system as that is what is orbiting the sun, not the Earth).
Rotation part:
Even though you sit facing your desk and looking out the large window on the other side of the desk for 24 hours without thinking that you are rotating you are in fact rotating. For example, you see the sun rise and about half a day later you see it set thru the window. Now for most of man's history it was thought that you were not rotating and that the sun was going around the Earth, but I am assuming you know better than ancient man did. Thus, you are rotating even if sitting at your desk with both your hands glued to the desk. Your rotational rate is 15 degrees/ hour.
POINT of this example:
Is that you should "look to the heavens", not your local enviroment, to tell if you are rotating or not.*
(Leaving the example and returning to the ant on the ball):
Yes, it sure seems to the ant (from his local obsservations) that he is not rotating, but this is a very intelligent ant. He knows how to tell if he is rotating or not. He saw the string sweep out a 360 degree circle in the heavens while he made one orbit around the "larger object" so he understood that despite the local appearances, he was rotating.
Please be smarter than ancient man and as smart as that ant.
PS to Janus58:
For god's sake let them continue to think the moon is orbiting the Earth. - I am not up to showing that is an erroneous concept. (One I held until you explained the error to me. - thanks again for doing so.)
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*Initially I had "must" instead of "should" in this sentence and only changed as it is not technically true with "must." (If you could precisely measure gravity at all points of interest and exactly determine the shape of a liquid surface, you could also tell if you were rotating, even if you could not observe the heavens. - Think what shape water takes in a bucket if it is rotating water to understand the point.)