What happens to a spinning rod with a ball inside?

[Adikshith Ojha]

OK, this is not a homework problem, I was simply fooling around when I conjured this up. And I guess I must include that I'm only a beginner to physics so my knowledge is limited. Now, for the questions.
Say there is a hollow massless rod, and inside it you have a ball of certain mass, the radius of the ball is equal to that of the rod and there is no friction between the two surfaces. Now if I were to keep it on a table and give it a spin, will the ball remain in centre or stick to one of the ends of the rod? My intuition tells me it would stick to one end but I'm not 100℅ sure about it. OK, now for the real one, now consider the same rod and throw it keeping it vertically in such a way it does a combined rotational and translational motion, does the ball keep going up and down as the rod spins? Or again, does it stick to one end? I'll again guess here that if I give it a certain angular velocity such that the centrifugal force overcomes the gravitational force, it would stick to one end (keep in mind that I have assumed the ball to be in one of the ends when the motion is just about to begin, does it change if the ball is at the centre when the motion is just about to begin?) Assuming my guess to be correct, say I give it an angular velocity that is not enough to overcome gravitational force, I assume the ball keeps moving from one end to the other as the rod rotates, so essentially, the centre of mass is... Oscillating?... Anyway, What would be the motion described by the body in such a case? And if my guess is wrong, how would the motion be? I know that I have posed quite a few questions but I would be very grateful if I could get the answers for them. Thank you.

 

[andrewkirk]

You need to give the rod a mass, otherwise its presence in the problem becomes irrelevant, since once the motion is underway it cannot impart any force on the ball - a massless object cannot impart a force on a massive object unless the former is firmly attached to a different massive object (eg a massless cricket bat held by a massive batsman can impart a force on a massive ball).

It seems by implication that you are assuming the ball starts off in the centre of the rod, although you do not clearly state that. I will assume it is initially in the centre. Answers may differ if it is not.

In the first situation on the table the ball will remain in the centre.

In the second situation, as long as the initial velocity of the centre of mass of the rod is the same as that of the ball, the ball will remain in the centre.

I don't understand what you mean by your third scenario. It needs a more precise description.