Unformatted text preview: with itself is zero, and since is entirely in the direction of , the cross product of these two vectors is zero also. Since angular momentum does not change over time it is conserved. This is essentially a more general expression of Kepler's Second Law, which we saw ( here ) also asserted the conservation of angular momentum. At some time t , we have the position vector and velocity vector of the motion that define a plane P with a normal given by = × . In the previous proof we showed that × does not change in time. This means that = × does not change in time either. Therefore, × = for all t . Since must be orthogonal to , it must always lie in the plane P ....
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 Fall '10
 DavidJudd
 Physics, Angular Momentum, Force, Gravity, Mass, General Relativity

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