When a spinning spherical mass also possesses significant translational motion, the situation becomes a little more complex. Only the mass of the body will be analysed under this condition. Other parameters will exhibit similar characteristics.

w^/ is now the spin rate in axes moving translationally with the body.

The mass of the elemental at rest is given by (2.2) so that the energy mass of the elemental in this scenario is

First, take a relativistic approximation of the second term of the denominator retaining only second order terms. This gives simply

Now take a second relativistic approximation again retaining only second order terms. Thus

Integrating (2.49) with respect to f gives the energy mass of the toroid

Finally integrating (2.53) with respect to r gives the energy mass of the sphere thus

Converting this to a standard relativistic mass equation via an approximate binomial contraction gives

For the purpose of determining the energy mass of a spinning spherical body also possessing a linear motion, it therefore appears that, in a second order relativistic approximation, the two separate velocities, each at their own individual mass effective dimension, are simply added together as orthogonal vectors.

Note that because of this combination of the two velocities, the limits to which each can be theoretically increased is reduced. In particular, if v is large enough, it would not be possible to increase w such that wG® c.