problem link
http://knol.google.com/k/alex-belov/...xmqm1l0s4ys/9#

The idea is very simple.

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

Each piece has constant angular velocity. Each piece of ring has
variable linear velocity at surface point. Once per circle each
element of ring stop on surface. At surface point this element has
linear velocity value equal to zero.

The ring must be broken in one location and one element of chain which
has a zero value of linear velocity holding by the surface. This is
not mean to stop the whole ring at this time. This mean stop the red
piece and cut the ring at the same time. The surface holds just one
element of ring and other elements of chain is continuing movement by
own trajectories.

If calculate net linear momentum of these elements then this net
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 has been join to the surface and mass is M
(suface) + m(element). Set of elements has a mass equal to (n-1)*m
now. It=92s change initial condition. The surface is still keeping same
momentum and increase own mass. But chain (set of elements n-1) should
hold same ring initial momentum.

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

Would set of n-1 elements return whole ring momentum back to surface?

Will this surface return to initial velocity?

On Jun 26, 1:41*am, Alex wrote:
problem linkhttp://knol.google.com/k/alex-belov/paradox-of-classical-mechanics-2/...

The idea is very simple.

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


So, our system has mass nm, angular momentum L = \Sum_i r_i \times
mv_i, and Linear Momentum P = \Sum_i mv_i

Each piece has constant angular velocity. Each piece of ring has
variable linear velocity at surface point. Once per circle each
element of ring stop on surface. At surface point this element has
linear velocity value equal to zero.

Incorrect. A ROLLING ring has angular momenta, not linear. Thus,p =
0.

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."
Please read and look on knol site for details.
http://knol.google.com/k/alex-belov/...xmqm1l0s4ys/9#