Science a GoGo's Home Page Forums General Discussion Physics Forum A rolling ring on surface. How to solve a problem?

If spit a rolling ring to small parts of n elements array (1,2,3,...,n) with mass m then each of them conduct linear and circular movement on surface.

Each piece has constant angular velocity and variable linear velocity. Once per circle each element stop on surface. Value of linear velocity of this element is zero at this time. If break chain then all of these elements except one is continue to move. If calculate net linear momentum of these element this should be equal to this ring initial linear momentum. But one of these elements is stop already and net momentum will be for n-1 elements. In this case one element attached to the surface and mass is M(suface) + m(element). Array of elements has a mass equal to (n-1)*m. It’s change initial condition. The surface is still keeping same momentum and increase own mass. Array of elements should hold same momentum, but lost one piece with mass m.


Is this net of linear momentums for n-1 elements array with mass (n-1)*m is equal to the ring initial linear momentum?


The surface is still keeping same momentum and increase own mass. Array of elements should hold same momentum, but lost one piece with mass m.
A few elements will return back small value momentums to surface and increase surface mass.

Will other elements with own momentums compensate surface momentum with new mass value?

How to solve this problem?

Picture and problem description there
http://knol.google.com/k/alex-belov/paradox-of-classical-mechanics-2/1xmqm1l0s4ys/9#

I don't know where you guys are getting this cra* at but
I hope you dont carry it into the field , if you ever get there.

you cannot create mass (.)
you cannot increase mass.
no matter what your instructor says.
or what the web site says.

the ring that is split into separate rings will still
have the same combined mass.

if you were to squeeze jupiter into a baseball sized planet , its mass would not change , if you were to divide jupiter into 20 separate planets , the combined mass would not change.

your link did not work so I could not explore the problem
you spoke of , and I could not understand exactly what you were trying to put across.

What do you mean?
BTW did you understand this problem?
One more time for ...
A rolling ring(chain of n element)on surface.
One of this element all the time has value of linear velocity ZERO at surface point(READ physic BOOK)
When ring stop, just n-1 elemet has a linear velocity more then zero.
For better undestandig chain is broken at this moment.
The question is: would this chain contain a linear momentum is equal to initial ring momentum?

P.S.
There is no reason create a post and say "I don't know".
The wolrd find out answer.

if you could be a little clearer , about this , it seems that you want to have a rolling ring , that is stopped that has zero linear velocity , and a rolling ring that stops , and after it stops it has a linear velocity more than zero.

in my world if a rolling ring is not rolling , it has no linear velocity.
if it has no linear velocity , it has no linear momentum.




for better understanding , I need to see a picture of what you are trying to put across here.



I assume you mean , would these rings contain a linear momentum equal to initial ring momentum?

my answer would be , the rings contain zero linear momentum.

the linear momentum that the rings initially had , was transfered to the surface as they stopped , the amount of linear momentum transfered to the surface would depend on the amount of friction loss between the rings and the surface they were rolling on before they stopped.


I finally got the web page link to open ...

I could not understand it either.

but at the top , there was this question.


laws are meant to be broken.
but usually its the wording of the laws that are flawed.
you actually don't break any laws , you just define the laws further , making them better.

Definitely, you don't not understand this problem.
Center mass of ring has a constant linear velocity at surface point.
Any element or ring has a variable velocity at surface point.
Any time ring stay on surface. This point which contact to surface has linear velocity zero.
This is a regular classical mechanics. Or you didn’t know about it?
Stop chain by surface. This means hold one element of chain which has zero linear velocity at surface. Not stop whole ring. Just one element of ring and let other elements of chain continue to move. To let them move ring must be broken at this point. Other elements must return initial ring momentum to surface, but mass of this chain is already less then initial ring mass. One element already stopped and it part of the surface now.

--
I’m sorry. But Idea is very clear and simple.
Thank you for your attention.

If describe to me to you witch stop?
I you agree!
left you for explain , ok sorry I for not.

Well.

Take one element with zero linear velocity. One element on the ring's bottom Close to surface
Glue this element to surface. That's it.
Let other elements to move

Please for me to explain my apoleagee , in case of this one exception is for the ring seperated into many parts and to glue the one part to surface , is I in this one correct?

allow the unglued parts of ring to rotate as bearing roller
inside outer glue ring.

of course I understand what!!! you think Im idiot?

yes please let other elements to move in spacial distance between other parts .

I now see where the prob was.

Easy to imagine this ring like a chain.
Each element join to others, but has free position movements. If hold stopped element on the ground(glue for example) then other chain elements has free position movements. Simple problem, just one element joint to surface initially and other elements of chain must return initial momentum to the surface. But surface and chain masses has been changed.
On complexity, each stopped element will join to the surface. All these elements will lie down on the surface on the the end. But time for this action for each element is different. Each element has same mass, but different linear momentum. In this case, the surface mass will grow faster than ground will recieve all momentum back.

My suggestion:

If ring has set of n elements then for surface point only ring's set of n-1 elements is always move. But one element with zero value of velocity stand down and it will be always part to surface.

For this particular case, this set of n-1 elements (broken thin ring or chain) not equivalent to set of n elements (initial ring). Base on law of momentum conservation net momentum for set n-1 elements would have same initial momentum, but momentum density for each element of this set n-1 will change. The surface will take all elements momentums back when they’ll stop. Base on law of momentum conservation, from same momentum the body with higher mass will take lower velocity then body with lower mass.

P=m*V

m1*V1=m2*V2

The surface with new mass will take a velocity V1 from set of elements n-1. This velocity is different from initial surface velocity V0, because the surface mass has been changed.

Follow the law of momentum conservation, even all element of broken ring will stop on the surface, this surface will have linear velocity more than zero.

Just keep in mind. This model has 3 phases. Bodies at phase1 is different from bodies at phase3. The law of momentum conservation works, but it gives different result for bodies with different mass.

This is the comment from other forum.

"If the platform is completely free to move (say floating in outer space) momentum conservation requires that it will end up with a positive forward velocity V=(nm/(M+nm) )v. Kinetic energy is not conserved because as each link slaps down on the surface some energy is converted to heat.

For a full ring rolling at constant velocity there's no horizontal force between the bottom of the ring and the surface but that requires the ring to be balanced (rotationally symmetric). As links become missing from the circle that's no longer true so the succeeding links that hit the surface do have a forward pull on them accelerating the platform forward."

I think this is a clue for understanding.

The element with zero values of linear velocity on the surface is too small. Mathematically the geometrical size of this element strives to zero. However, this is the physical element, and it has its own geometrical size.

http://knol.google.com/k/alex-belov/paradox-of-classical-mechanics-2/1xmqm1l0s4ys/9#

For this model, а repulsion and а collision comes on different planes.

The vertical plane doesn’t have any contacts with the rolling body.
Otherwise the horizontal plane always has a physical contact with rolling body.

From vertical plane point of view, all elements of rolling body have a movement.
If calculate a rolling body translation momentum with respect to vertical plane then all elements of rolling body must be included.

Otherwise if look on horizontal plane, one element of rolling body stays on the surface all the time.If calculate a rolling body translation momentum with respect to horizontal plane then one element of rolling body must be included to the mass of horizontal plane.

erm, kinetic energy converted to thermal energy until state of momentum is broken. Clang clang, ring at rest? Summink like that anyway.