worksheet08 - Worksheet#8 PHY102 Motion in a potential...

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Worksheet #8 - PHY102 Motion in a potential Although you first learn about Newton’s second law ~ F = m~a and the dynamics that results from it, much of the discussion in the more advanced physics texts is in terms of “potentials” V ( ~ r ). A particle undergoes motion “in a potential”. Note that V is a scalar , while ~ F is a vector. It is often easier to work with the potential unless you are forced to work with the force. Actually even motion in a potential is carried out using Newton’s second law. However visualizing the potential is very helpful in developing physical insight into the trajectories. It is also useful in understanding thermodynamic processes, which are statistical in nature. Anyway for our purposes, we just need to know how to relate the the force to the potential, and that is via the equation: ~ F ( x, y, z ) = - ( ∂V ∂x , ∂V ∂y , ∂V ∂z ) (1) Often it is easier to work in polar co-ordinates ( r, θ, φ ). If we work with central potentials , V ( r ) which do not depend on the angles ( θ, φ ) things are
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