Consider Coriolis force or not?

[AntonPannekoek]

Hello, my question is very short. I have a spinning bar, with a small ring threaded. I know that for analyzing the problem I have to consider the centrifugal force that makes the small ring go away from the center. My question is do I have to also consider the coriolis force? : - 2m (w x v'), or is that force in equilibrium with a normal from the side of the bar?

 

[jbriggs444]

It depends.

What do you know, what are you trying to calculate and how accurate do you need the result to be? As is always the case, those questions control which factors you must consider and which you can neglect.

 

[AntonPannekoek]

It depends.

What do you know, what are you trying to calculate and how accurate do you need the result to be? As is always the case, those questions control which factors you must consider and which you can neglect.

I need to find the equation of the motion of the ring.

 

[jbriggs444]

I need to find the equation of the motion of the ring.

What do you know, what are you trying to find out and how accurate do you need the result to be?

Let me put it another way: Do you know the mass of the bar? Do you know the mass of the ring? Are you told that the mass of the ring is negligible compared to the bar?

Do you know the coefficient of friction of ring on bar? Are you told that it is zero? Do your accuracy requirements mean that not knowing that coefficient is a problem?

Do you know the rotation rate of the bar? Are you to assume that it is fixed? Is the bar anchored to a pivot or is it rotating freely?

 

[AntonPannekoek]

What do you know, what are you trying to find out and how accurate do you need the result to be?

I guess not very accurate, I also have the initial position and velocity of the ring. and the angular velocuty of the bar.

 

[jbriggs444]

I guess not very accurate, I also have the initial position and velocity of the ring. and the angular velocuty of the bar.

If the angular velocity of the bar is fixed then it is true that the net of the Coriolis and normal force can result in no tangential motion relative to the rotating frame. The ring must follow the bar. F=ma. No tangential motion, so no tangential acceleration, so no net tangential force. That answers the original question.

[Also note that no tangential motion in the rotating frame means no radial component for the Coriolis force]

If one ignores friction of ring on bar (and continues to assume a constant rotation rate about a fixed center) then it is true that this means that Coriolis is irrelevant to the radial motion in the rotating frame.

These may (or may not) be appropriate simplifying assumptions for the problem.

 

[vanhees71]

My recommendation is to use the Lagrange formalism and also to post such questions in the homework forum! It's a standard problem in many analytical-mechanics textbooks by the way.