  We show that the concept of total variance of a spin state, defined as the
average of the variances of spin projection measurements along three orthogonal
axes, also gives the rotational speed of the state in projective space,
averaged over all rotation axes. We compute the addition law, under system
composition, for this quantity and find that, in the case of separable states,
it is of simple pythagorean form. In the presence of entanglement, we find that
the composite state "rotates faster than its parts", thus unveiling a
kinematical origin for the correlation of total variance with entanglement. We
analyze a similar definition for the acceleration of a state under rotations,
for both pure and mixed states, and probe numerically its relation with a wide
array of entanglement related measures.
