![]() The system has no reason to give one component of kinetic energy more energy than any other component. The set of all possible vectors with a given magnitude is the formal definition of a sphere, so that’s where we get the sphere. If we look at the equation for kinetic energy, it only contains the magnitude of the momentum, so any momentum with that magnitude is possible. Why Does a Sphere Show up in the Derivation? We can say that if we have twice the volume, we have twice the number of positions as we did before, so we can say We won’t be able to get an exact number of all possible positions since space is continuous (as far as we know).
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