John2020

Your argumentation is all about an inertial frame. I speak about the rotating frame. So there it cannot be towards the center since there we have the centrifugal that is greater than the centripetal during the increase in angular velocity.

You mean about the Euler force?

That cannot be true along the rigid rod (we speak always about the mass m accelerating radially).

But the Euler force is being developed along the axis of rotation. We don't have any mass there that would be influenced. That could be utilized if the mass m and the rod would on the z-axis (as seen from screen). It means the rod and the mass along the axis of rotation of mass M. It is a good alternative for my next challenge. Don't forget I speak for the transition time where the centrifugal > centripetal and not while they are equal (thus zero acceleration).

Before I wrote those points, I mentioned "Rotating Frame (Fictitious Forces)". So, for the rotating frame it will be outwards as also the accelerometer (we speak always for mass m) will show the same direction.

I don't understand what you actually mean. Both are provided by the motor (inner mechanism, power etc) and transferred through the rigid rod.

Being inside a car driving in a curve you are in a rotational frame that implies what you experience is a centrifugal force that creates a pretty physical outwards acceleration when you are on board. There is a problem here. In both cases the coordinates of the mass m will appear away from the center because we have a change in angular velocity. How you say the acceleration is towards the center in both cases? Such claim brings the inertial and rotational in disagreement. I suppose this is a mistake in your description. I would understand the above for the inertial frame, however when we are in the rotating frame the role of varying centripetal (the difference actually between two subsequent angular velocity values) is taken by the varying centrifugal force. There are some points that for me up to now have no satisfactory explanation as given from your side (as forum). Rotating frame in my example (fictitious forces) a) The role of centripetal is taken by the friction force b) When the angular velocity is constant, the centripetal and the inertial centrifugal force are equal that keeps the mass at point r1 or moves with constant velocity (assuming to be very small due to limited rod length) c) During the transition to a greater angular velocity value, the centrifugal becomes greater than the centripetal d) Due to (c) the mass m will acquire a radial outwards acceleration (since we have a change in angular velocity) e) Due to (d) for a mass ratio e.g. M/m=10/1, the CoM changes and accelerates in the same direction as the mass m Conclusion: Since the acceleration of mass m is caused by the inertial centrifugal force (considered fictitious), there will be no counteracting force upon the rest of the system that implies a change and acceleration of CoM of a system is feasible. Note: swansont assumed m<<M in his analysis so there will be no change and in CoM that is OK.

Then how you explain the acceleration of mass m? The fact we experience the centrifugal force while being in a car driving over a curve, it is a physical effect. Otherwise, it is like being in denial that inertial forces exist. What I agreed was we don't have fictitious forces in an inertial frame.

The obvious can be identified in the rotating frame easily: On my example as long as the angular velocity changes, the centrifugal force increases (net force is not null -> centrifugal > centripetal) results in accelerating mass m radially. At that particular time frame this change is not counteracted by a force upon the rest of the system because the centrifugal is by nature inertial (not a real force. If it was a real force then I would agree with you. This is the point you all miss.). Thus, the acceleration of mass m results in an accelerating change of the CoM of the system as a whole.

In our case you overlook an important detail, there is a mass transfer that implies an accelerating change of the CoM. The situation has nothing to do with the normal forces and the table. You are fantasizing things that do not hold. Lastly, I am not hoping someone will eventually say, "no", but to acknowledge the obvious. Next time, I would suggest you to make the same exercise with the hammer (as Ghideon proposed) or to think the situation of a passenger in a car while is taking a curve by changing the speed slightly..

I didn't say that. The problem is I searched in the entire web to find physics exercises that address this kind of problem (as I proposed with my last drawing), however I found none. Do you have any resource that may show a detail solution to this specific problem (non-rotating and rotating frame of reference)? When something does not fit well, I have always doubt (and eventually I am right about it). I need a detailed and clear mathematical analysis based on classical mechanics (No Lagrangians, no Hamiltonians and stuff). If you have any resource on this, please share it with us. The way we handled this problem through the thread was 99.9% based on texting and not maths, meaning what we exchanged was just views/interpretations, no proofs and no real life observations. No thanks. I already learnt a lot. When you make the analysis on the rotating frame, I am convinced 99.9999% that your view on this matter will be wrong because you follow of what is familiar to you, thinking that will never fail and you will ensure that you will not get embarrassed (don't forget you are a member of this forum having a good reputation). That does not mean anything. Those who know very good physics may fall into the trap of not questioning something for many reasons even if there is a small doubt on their head because of an observation/experience (equals experiment), however they afraid to express it publicly over the forum. It would be like being against the stream. Unfortunately, most humans are afraid more of their reputation (especially when one is specialist on the field) than to explore something that may look initially far-fetched or ridiculous. Next time, take the hammer with the short leather grip (semi non-rigid) and make the experiment by yourself. I suppose there will be enough centrifugal force left in the rotating frame that will show you the way forward (enlightenment).

This is the simplest example I could imagine. No worries. If I am wrong then I am wrong. However, I suspect if you make a careful analysis in the rotating frame, maybe what I proposed will start to make sense. Anyway, if all other participants are of the same opinion like yours then I have nothing more to add. Good night and be well!

OK. I would like to see from you (or anyone still interested) the analysis in the rotating frame. I am curious, what kind of justification we may have there.

I already did. I am expecting no reaction upon the rest of the system while the mass m is being accelerated because the acceleration of the mass m is caused by the increasing centripetal (by subtracting the kinetic friction force). In other words, the change in centripetal appears as an inertial force in the inertial frame that by nature has no counter part (reaction force). The same I expect to happen in the rotating frame but now with the centrifugal force that is by nature inertial having no counter part (reaction force).

Do you speak seriously? How can that be? The rod cannot move radially, thus cannot pull. If it helps then let us make a version with massless rod. I am not expecting to have a reaction force in this case. When we make the analysis in the rotating frame, the same conclusion is expected according to my view (in the rotating frame is clearer why there will be no reaction). When we have to compare both analysis, either we should have a reaction or not at all, in order the observations to agree.

I don't think is the same question. On top of page 18 we have a device. I invite you to make an analysis and give your answers to (a) and (b). Are you in?

The rod accelerate the mass m? I don't get it. I don't know where it will help if the rod is massless. But then we will have no friction. You can join the conversation if you like.

This is all well known. I am still speaking about a radial reaction force. Is there any opposing force (upon the rest of the system) to centripetal? The centripetal is the cause behind the radial acceleration of the mass m in the inertial frame. Where is the reaction upon the rest of the system?

I am speaking about a radial reaction component. Is there any?

The centripetal has direction towards the rotor, right? Where the other applies?

While accelerates radially is there a reaction force upon the rest of the system?

The mass slides accelerating or with constant speed?

This is very clear, no fictitious forces for the inertial frame case. As I said, I am not comfortable with the frame of references, however Ghideon helped me to understand something (it requires more exercising from my side). Now, if you wish you have to do the non-rotating frame analysis. I forgot to ask you what is the answer for (a) and (b) by the way for the case of the inertial frame? Will mass m accelerate or not? Will the system (M+m) accelerate in the same direction or not?

Of course the object is rotating. How you are going to make the analysis has nothing to do with me. The goal/challenge is (as we agreed with Ghideon) to analyze this system from an inertial frame of reference as also from a rotating frame of reference and then to compare the results.

From the moment the friction plays the role of the centripetal, before we increase the angular velocity the system is in equilibrium that means the centrifugal equals to the centripetal. Increasing the angular velocity the net force will have an outwards direction that implies centrifugal is greater than centripetal. Of course, the centripetal will increase too, however as long the angular velocity increases, the centrifugal will be greater than the centripetal. Moreover the centripetal has a direction towards the center of the rotor and the net force is outwards, otherwise mass m acceleration to the right cannot be justified. Additionally, the rotor is not fixed but in outer space.