http://en.wikipedia.org/wiki/Impulse_(physics)

Then it's a silly question. The rotation of the sphere makes no difference. It might as well be a stationary lump of coal.

You would have thought someone would have pointed that out earlier.

Oh, hang on, I did.

However far I am from the sphere, only the particles that form a circle exactly on my line of sight are moving perpendicular to me. Their number is constant.

So there's no evidence that the sum of the speeds is zero.

More importantly, they may have zero velocity from my point of view, but they still have exactly the same speed as the others.

Apart from particles on the axis, every bit of the sphere traces out a circle. The radius of that circle is the distance from the particle to the axis. The circumference is 2 pi times that and it travels that distance each time the sphere revolves.

That fixes the distance it travels, and the time it takes to do so. So that sets its speed.

Averaging that over all particles will give the mean speed.

There's nothing there about how far away from it I (or you) might be.