What Makes a Sliding Book Stop Both Rotating and Translating Simultaneously?

[.Scott]

If your graphics does not 'translate' to equations then it may be that there is something wrong somewhere.

I think I translated it successfully. It's just not the most fluent thing I do. Some of those ratios (for example 4/3) are based on simple integrations of circle area - once for spin, once for translation.

As you can see in the previous post, I have also redone the program to report energy loss instead of force. This hasn't affected the "translate" (or "travel") column because there's a straight speed factor and the energy loss is scaled to speed anyway. But it made a difference with the spin column.

 

[Dadface]

The assumption still seems to be that translational and rotational motion stop at the same time. Where is the evidence to back up this assumption? I suggest that respondents here try out a few preliminary tests for themselves. There are many variables to consider but in the first instance all that is needed is a flat surface and objects that can slide and rotate over it.
I have tried it out with different things and I am not at all convinced that both types of motion stop simultaneously. Try an object or book with a smooth surface and put a lot of spin on it.

 

[voko]

There is quite some literature on the subject. This has even been the subject of at least one doctoral dissertation. The short answer is yes, friction couples rotation and translation and they both stop together. The final ratio between the linear and angular speed depends on the shape and mass distribution in the object in question. Some references:

A. Yu. Ishlinskii, B. N. Sokolov, and F. L. Chernousko, Motion of plane bodies with dry friction, Izv. Akad. Nauk SSSR, Mekh. Tver. Tela, 16 (4) (1981) 17-28

K. Voyenli and E. Eriksen, On the motion of an ice hockey puck, American Journal of Physics 53, 1149 (1985).

S. Goyal, A. Ruina and J. Papadopoulos, Planar sliding with dry friction. Part 1. Limit surface and moment function, Wear 143, 307–330 (1991).

S. Goyal, A. Ruina and J. Papadopoulos, Planar sliding with dry friction. Part 2. Dynamics of motion, Wear 143, 331–352 (1991).

Z. Farkas, G. Bartels, T. Unger and D. E. Wolf, Frictional Coupling between Sliding and Spinning Motion, Phys. Rev. Lett. 90, 248302 (2003). [http://arxiv.org/pdf/physics/0210024.pdf]

Guido Bartels, Mesoscopic Aspects of Solid Friction, PhD thesis, 2006 [http://duepublico.uni-duisburg-essen.de/servlets/DocumentServlet?name=duett-01272006-083621/]

Mark Denny, Comment on “On the motion of an ice hockey puck” by K. Voyenli and E. Eriksen, Am. J. Phys. 74, 554 (2006)

I would recommend reading at least the paper by Farkas et al.

 

[.Scott]

Z. Farkas, G. Bartels, T. Unger and D. E. Wolf, Frictional Coupling between Sliding and Spinning Motion, Phys. Rev. Lett. 90, 248302 (2003). [http://arxiv.org/pdf/physics/0210024.pdf]

I would recommend reading at least the paper by Farkas et al.

Farkas found the asymptotic ratio to be 0.653, a lot less than my 0.865. I believe him.
The key thing is that we both agree that there is a value will always be approached as the disc slows. That, om general, the pivot point draws out a spiral, not a circle, onto the disc.

 

[Dadface]

There is quite some literature on the subject. This has even been the subject of at least one doctoral dissertation. The short answer is yes, friction couples rotation and translation and they both stop together. The final ratio between the linear and angular speed depends on the shape and mass distribution in the object in question. Some references:

A. Yu. Ishlinskii, B. N. Sokolov, and F. L. Chernousko, Motion of plane bodies with dry friction, Izv. Akad. Nauk SSSR, Mekh. Tver. Tela, 16 (4) (1981) 17-28

K. Voyenli and E. Eriksen, On the motion of an ice hockey puck, American Journal of Physics 53, 1149 (1985).

S. Goyal, A. Ruina and J. Papadopoulos, Planar sliding with dry friction. Part 1. Limit surface and moment function, Wear 143, 307–330 (1991).

S. Goyal, A. Ruina and J. Papadopoulos, Planar sliding with dry friction. Part 2. Dynamics of motion, Wear 143, 331–352 (1991).

Z. Farkas, G. Bartels, T. Unger and D. E. Wolf, Frictional Coupling between Sliding and Spinning Motion, Phys. Rev. Lett. 90, 248302 (2003). [http://arxiv.org/pdf/physics/0210024.pdf]

Guido Bartels, Mesoscopic Aspects of Solid Friction, PhD thesis, 2006 [http://duepublico.uni-duisburg-essen.de/servlets/DocumentServlet?name=duett-01272006-083621/]

Mark Denny, Comment on “On the motion of an ice hockey puck” by K. Voyenli and E. Eriksen, Am. J. Phys. 74, 554 (2006)

I would recommend reading at least the paper by Farkas et al.

I can't take the work of Farkas et al and others seriously yet because because their findings do not conform to simple observations I have made. Where is the experimental evidence that both types of motion stop simultaneously?
I have done simple tests on my desk top and in many cases with different objects the motions do seem to stop at the same time. But not in all cases. I am able to put a lot of spin on a light weight, smooth covered book at the edge of my desk whilst sliding it towards the middle of my desk. Each time it seems to stop sliding long before it stops spinning. try it for youself.

 

[voko]

The Farkas paper deals with a uniform disk specifically. Bartel's thesis is more generic, and he shows that for some mass distributions the terminal motion may be pure rotation. See Fig. 3.10.

 

[Dadface]

Just tried it several times with a disc shaped lid from a storage jar and in each case both motions did seem to stop at the same time. Will try different variations later.

 

[MikeGomez]

Just tried it several times with a disc shaped lid from a storage jar and in each case both motions did seem to stop at the same time. Will try different variations later.

That's because your desk surface and/or the book (or disk) is not perfectly flat.

It just takes a very slight imbalance in the smoothness of the contact surface to throw the whole experiment off. Unless you can verify the smoothness of both the book and desk with high precision, the heavier book experiments are more valid because they are not quite as sensitive to small imperfections in smoothness.

This "catching" effect is even more pronounced if you are using a lid or any kind of ring shape instead of book or flat disk shape. Friction pressure gets localized instead of being spread out over the entire object.

 

[.Scott]

I can't take the work of Farkas et al and others seriously yet because because their findings do not conform to simple observations I have made. Where is the experimental evidence that both types of motion stop simultaneously?
I have done simple tests on my desk top and in many cases with different objects the motions do seem to stop at the same time. But not in all cases. I am able to put a lot of spin on a light weight, smooth covered book at the edge of my desk whilst sliding it towards the middle of my desk. Each time it seems to stop sliding long before it stops spinning. try it for youself.

The Farkas paper does include experiments. They used CD discs, data side down.

 

[Dadface]

The Farkas paper does include experiments. They used CD discs, data side down.

Yes I know. I scanned the paper. The initial observations I referred to were made were made with a book whose surface was smooth enough for me to set it spinning fairly fast whilst getting it moving with translational motion. I have since tried other things, including CD discs, but was unable to get these spinning as fast as I was able to get the book spinning.
Quite often the spinning /moving discs seemed to stop and then move momentarily in a different direction. There were also times when air pressure seemed to affect and slow down the movement. I assume this was due to the smoothness and close contact of the surfaces
There are so many variables to consider and pressure now seems to be another one.

 

[.Scott]

There are so many variables to consider and pressure now seems to be another one.

The high spin situation is especially sensitive to anything that varies from the ideal. For translational motion, you're creating a near frictionless surface, so any local valleys in the surface will affect a slow moving object. Any dust or smudge on the table or the disc could cause a snag. The spin will cause more heat along the edge of the disc than in the middle - giving the disc a slight saddle shape. Also, if the spin is not strictly horizontal, there may be a bit of precession.

 

[A.T.]

Friction on Ice is quite complex, and cannot be modeled with a constant coefficient.

Here is more on the physics of curling:

https://www.youtube.com/watch?v=7CUojMQgDpM

 

[sbstratos79]

hehe, I skipped pages 3-7 of this thread. But didn't jbriggs444 nail it? :/ His/Her explanation seemed pretty convincing(to me atleast)