When velocity changes speed only, work/energy is involved. But when only direction changes, no work/energy is involved- as in the centrifugal/centripetal acceleration of a rotating mass at a contstant curvature and velocity/energy. How does this impact the definition of velocity as the time integral of acceleration. Is time not changing in one case and not the other?
Time is always perpendicular to the radius vector. This makes time and space cyclic quantities (frequency). Rotating system has angular velocity, which is frequency and is directed along the axis of rotation. My argument is that all isolated physical systems have their size-dependent period of rotation and this is the system-dependent relative time. Preprint Cyclic-time mechanics of isolated systems
Preston Guynn Please note that the work W=integ(F.ds)=integ(ma.ds)=0, as the acceleration a is normal to the direction of s in a circular motion.
Even with reflected billiard balls (elastic impacts) the energy of the billiard balls is constant. The conservation of momentum is independent of the conservation of energy.
Could you please explain what the question is?
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