# Elastic off-center central collisions (?)

"elastic off-center central collisions" (?)

Hi, I'm new to the forums and, to a large extent, to physics in general.

Anyway, I've been interested in the dynamics of simple collisions of spherical particles in 2D and 3D space.

I've been searching for information on the collisions of this type and to such ends I recently bought a book entitled "Handbook of Physics". So you know, it's a recent edition (copyright 2006).

So, to the specific question at hand:

The book entitles a particular section on collisions as "elastic off-center central collisions", but simultaneously defines the terms "off-center" and "central" collisions as follows (direct quote from book):

Central collision, the collision normal at the moment of collision points parallel to the connecting line of the centers of gravity. There is no torque...

Off-center collision, the collision normal does not point along the connecting line of the centers of gravity, hence there is torque. The bodies begin to rotate...

See the contradiction in the above? The section presumes to be about "off-center central collisions" but the given definitions of "off-central" and "central" contradict each other as far as torque is concerned.

Has the book juxtaposed some of it's terms? Or, perhaps there is something I am missing. The terms in the general local section are "straight-line collision", "non-central collision", "collision normal", "central collision", and "off-center collision".

Can someone who's physics savvy help me discern the nature of this dilemma? Do I just not know the terminology? It seems like a pretty blatant logical self-contradiction to me...

The confusion is detrimental in two respects: Firstly, I cannot know for sure what particle conditions they are actually referring to thus cannot select a situation to apply it to. And secondly, even if I did apply it the contradiction suggests the possibility of other errors.

Hopefully the information I have given is sufficient to resolve the matter, but if not feel free to ask me for more info, I'd be happy to provide it.

Your general perspective on the subject of collisions is of course also welcome.

Thank you for your time and for reading this thread. I await any replies you may have.

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NOTE:

I edited my first post on this thread to remove potentially distracting/excessive content.

The previous version perhaps made it sound like I was requesting info on all aspects of spherical particle collision, which would be a bit much for one thread. Thus I modified it to sound more directed and concise.

For reference, the modified portion of the previous version was (in it's previous form) as follows (with elipsis "..." indicating text beyond the part that was modified/cut):

...
Anyway, I've been interested in the dynamics of simple collisions of spherical particles in 2D and 3D space (will later extend studies to higher dimensions too). In particular I want to understand exactly how the collision effects the particles, including exact trajectories of the particles after collision, velocity, acceleration, and any and all exchanges of force, energy, and heat/deformation magnitude.

I emphasize that I seek real understanding of exactly how the quantitative formulas create the behavior and what they mean. I do not just want "the answer". Clarity and real understanding is important in the endeavors in question.

I've been searching for information on the collisions of this type and to such ends I recently bought a book entitled "Handbook of Physics". So you know, it's a recent edition (copyright 2006).
...

Once again, thank you for your understanding and time, as always.

Perhaps the full context of the section in question would be much more helpful:

I'm not sure if this is supposed to be on the internet, but I found a link to a pdf of the full text of the book (as far as I can tell it's the same edition).

You could take a look at the relevant pages. Perhaps the diagrams will help.

To find the pdf on Google I searched for "handbook of physics elastic off-center central collision", so you could use that method to get to it, or you could use the direct link below if it works:

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Doc Al
Mentor

I've been searching for information on the collisions of this type and to such ends I recently bought a book entitled "Handbook of Physics". So you know, it's a recent edition (copyright 2006).

So, to the specific question at hand:

The book entitles a particular section on collisions as "elastic off-center central collisions", but simultaneously defines the terms "off-center" and "central" collisions as follows (direct quote from book):

See the contradiction in the above? The section presumes to be about "off-center central collisions" but the given definitions of "off-central" and "central" contradict each other as far as torque is concerned.

Has the book juxtaposed some of it's terms? Or, perhaps there is something I am missing. The terms in the general local section are "straight-line collision", "non-central collision", "collision normal", "central collision", and "off-center collision".

Can someone who's physics savvy help me discern the nature of this dilemma? Do I just not know the terminology? It seems like a pretty blatant logical self-contradiction to me...
I have that book (an earlier edition), but never spent much time with that section (until now!). Looks to me like they butchered the definitions of the various collision geometries. At the very least the definitions of "central" and "non-central" should be contradictories (according to the rules of basic english)--not so here.

In any case, Section 2.6.2 "Elastic off-center central collisions" (in my copy) should probably have been titled: Elastic oblique central collisions. Central because the collision normal at the moment of collision points parallel to the connecting line of the centers of gravity (this is their definition); oblique (as opposed to direct), because the centers of gravity of the colliding bodies move in different directions (what they confusingly call "non-central"). Their use of "off-center" was a mistake.

I hope that helps a bit.

If someone has a reference for the "official" terminology for collision geometry, please share. (I'm digging through my library, but many of my books are still waiting to be unpacked.)

Indeed, oblique central seems a better description.

As you said, it's weird that their definition of non-central is not a logical negation of central.

One would think that simple logical negations would not be that hard to make errors on, but then again mistakes just happen sometimes.

I will be careful on the collision sections of the book then.

It would also seem wise for me to find a good second source of information on collisions, for cross referencing purposes.

Does anyone know of a particularly good document of simple collisions and the involved forces?

Also, if I may ask: When two spherical particles collide obliquely do they generate torque? Do one or both of the particles begin spinning? A point mass is not the same thing as a spherical object and I am somewhat unsure as to which of the two the book is referring to in that section. Does it depend on whether the objects have surface friction or not?