This is the law of momentum conservation for the translation with rotation movement:



This law has a complex number and it has linear and angular momentums.

Full momentum transfer for this movement has calculation by absolute value:


Full kinetic energy of rotation with translation movement is:




Follow law of momentum conservation and using complex number for translation with rotation momentum, the cylinders translation velocities have a different value on experiment 2.

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Base on previous statement it possible to say the translation with rotation movement is covering translation and rotation movements together. One of these movements is the simple version of main complicated movement.