If the rolling is "frictionless", like a tire rolling on a surface, you should be able to figure by just using the circumference... Actual translation of the sphere (the hypotenuse of X and Z components) divided by 2pi gives rotation about sphere's own pole in radians; then change that to degrees. (You undoubtedly know this; I'm trying to be complete.) But if the rolling is not meant to be nicely perpendicular (like a wheel skidding partly sideways), then you will have some friction, and the rotation can't be figured from the translation in any obvious way. You could apply an arbitrary friction coefficient, I suppose....

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