Rotational and translational motion can be described as a sum of 2 simple motions, which conducted in two separate events.
Then for translational motion equation is:
F_1=ma
Work for this type of motion which equal objects kinetic energy translational part is
E_k_t=mv^2/2
Base on third Newtons law symmetric force -F_1 is present for this event
Same for rotational motion with fixed axis equation is
F_2R=Ia
Work for this type of motion which equal objects kinetic energy rotational part is
E_k_r=Iw^2/2
Base on third Newtons law symmetric force -F_2 is present for this event
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Base on sum of two motions the full kinetic energy which is work of 2 forces is equal:
E_k_f=mv^2/2+Iw^2/2
Therefore sum of two symmetric forces for each simple motion necessary to initiate rotational and translational motion:
-F=(-F_1)+(-F_2)
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However, the modern classical mechanics says if force applied away from center mass of object then just force [tex]F_1[/tex] with symmetrical force -F_1 is enough to initiate rotational and translational motion with energy:
E_k_f=mv^2/2+Iw^2/2
How this part of force do this part of work Iw^2/2 - mystery.
This paradox base on suggestion what law of momentum conservation works always and adding symmetric force -F_2 is crashing this law.
If use
little rule where each motion law of momentum conservation should adequate force which induct this certain type of motion and all law of momentum conservation works locally, then not necessary hide force -F_2.
Center mass of isolated system is not the same as center of mass of objects and doesn't follow same rule.
Dark matter is not a mystery anymore. Just a miscalculation 
http://knol.google.com/k/paradox-of-classical-mechanics-2http://knol.google.com/k/alex-belov/the-wheels/1xmqm1l0s4ys/18
