The rectilinear motion of a body of matter is the only motion in which the effects of relativistic variation affect the whole of the mass identically and simultaneously. This is because the whole of the mass experiences exactly the same velocity magnitude at the same time. When the motion is along a curved path, different parts of the mass experience different velocity magnitudes. Therefore the relativistic effects are graduated throughout the body, along the radius vector from the centre of curvature to the path of the motion. When the radius of curvature of the path is much greater than the physical dimensions of the body, some relativistic effects can be treated as in the rectilinear case in an acceptable approximation. This scenario was briefly analysed in [1]. Clearly the greatest relativistic gradient effect occurs when the above radius vector magnitude is zero, and the mass is simply spinning.

This scenario is investigated in this paper for a spherical homogeneous mass. Parameters analysed for relativistic variability are mass, moment of inertia and associated radius of gyration, angular momentum, spin energy, volume, surface area, average matter density and circumference on the spin plane. While most of the effects are of mathematical interest only, there is one relativistic variation which may have significant implications in both the microscopic and macroscopic realms of existence. This is discussed at some length.

The effect of a combination of a rectilinear translational velocity and high angular rate spin on the relativistic mass is also analysed.

Also demonstrated in this paper is a new mathematical representation of centripetal acceleration.

It is assumed for the purpose of mathematical demonstration of the said effects, that the mechanical integrity of the spinning mass is not violated.

In the interests of brevity, unless necessary for complete clarity, a parameter will only be defined in this paper, if it has not already been so in [1] or [2] with which familiarity is assumed.