Expert: Daniel Mazur - 7/3/2009

Question
Hi Daniel,

The site won't allow me to ask more follow ups, but I am just not able to chew manythings. Not to say that I didn't get your explanations, they were fantastic I think.

When I asked the following ques:

"Also, according to the mechanism we discussed, there should be no linear motion, only this rotational motion, and that too about the axis passing from the other end of the square plank.... ???"

I understand that we consider both the linear motion and rotational motion of the thing in question.
I'm not confused with all this because I'm weak at the concepts or I haven't practiced problems, infact that's what I've been doing for past 1-2 years, doing problems, and I've sufficient practice in that now, I think.

What I don't understand is why does it have to be that way??
Why do we have to consider these two things??
What I mean to say is that when I apply a force on the point, the point tries to accelerate in a straight line but isn't able to do so because of the mechanism we discussed and ends up rotating. But why does the center of mass have to move forward. Nobody applied a force on it.....
I applied a force on the point and I witnessed the consequence, i.e. the rotation or angular acceleration but why the hell does COM go forward?? I didn't apply a force on that....why can't it be that the COM remains where it is and the thing just rotates about the axis through COM???

Also, you say that if the thing rotated about a non COM axis, then the COM would appear to be orbiting about that axis without the prescence of any centripetal force, but we can say so for any other point too.
Consider the body rotating about the COM axis, conserving the symmetry of nature, as you say; concentrate on some point apart from the ones lying in the axis itself, any point going around the axis. Even this point has no visible centripetal force, but still goes in a circle about the axis......

Cheers!
Shikhin  

Answer
Hi Shikhin,
My apologies for the problem solving suggestion, in your situation it's really redundant.

[quote] Also, you say that if the thing rotated about a non COM axis, then the COM would appear to be orbiting about that axis without the presence of any centripetal force, but we can say so for any other point too.
Consider the body rotating about the COM axis, conserving the symmetry of nature, as you say; concentrate on some point apart from the ones lying in the axis itself, any point going around the axis. Even this point has no visible centripetal force, but still goes in a circle about the axis......[/quote]

No. While using the model of mass points is useful, we mustn't mix up the arguments that we use in that model with the arguments we use when considering the whole physical body... As in fact THREE things are mixing here, two models and one reality, and our argumentation must keep them separate. Otherwise nothing can work well.

The model:
The plank does NOT exist, only a massive point exists. This massive point inherits from the real world the mass of the plank and the position (where the COM of the plank would have been) and its free motion (speed may not be zero if the plank moves linearly to start with). In this model no object may rotate/twist, because objects are dimensionless massive points. So here the plank can only move forward. These massive points may stay put, move linearly at constant speed, linearly accelerate or accelerate on a curved path (orbiting is a special case of the last mode).

The 3D body model:
The plank exists, it has not only mass and COM-position, but also positions of all the other points (these are NOT necessarily atoms, I am trying to persuade you) with a defined coupling between them. For our purposes we talk about RIGID body, which says that in a system of coordinates fixed to the plank, all points have fixed positions no matter what forces or torques are applied. Now, as this is a DEFINITION of the body (no matter what interaction it is that provides the rigidity), the COM and the rest of the body much accelerate as soon as force is applied at ANY point of the plank. The body will both accelerate linearly and rotate, while the relative amount of each will be given by the m, J, and the distance d of the point of applied force from COM. Once again, this model body is rigid by definition, so it cannot fly apart.

The 3D real life:
Compared to the 3D model, all we need is an internal interaction between parts of the plank, so that the plank is at least approximately rigid. We find this interaction in the electronic bonds, although these bonds are NOT of just one kind. We recognize three or four basic bond types: ionic, covalent, van der Waals and hydrogen bridging. That's at the interatomic level, inside the atoms the electrons hold on their orbits thanks to balancing the electrostatic attraction of the nucleus by obeying the Fermi statistics, nuclei hold together thanks to the strong interaction... There is a number of forces. They are internal forces and as such they don't directly influence the motion of the body - internal forces can never be considered "applied" at the body as a whole. Only because the forces are not infinite, the body will deform slightly upon rotation or linear acceleration, which changes J slightly and that in turn will change the rotational velocity.

The centripetal and centrifugal forces acting on every atom are in balance if, and only if, the free rotation happens about COM. If you make the thought experiment of applying force on plank in X at some finite distance from COM, keep reducing the distance and ASSUME that the response will only be rotation, then you will run into a singularity: as distance decreases, the rotation will occur less (torque is getting smaller), but there will be no linear motion. Then if you press exactly at COM, there will be no effect whatsoever. This is not consistent with our observation, so it cannot work as a plausible model for our Universe. This statement, just like others above can be written down in mathematical terms, but I doubt this will clarify anything more than words.

I hope a bit of what I wrote will help you get there...
Cheers,
Daniel