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Re: [Phys-l] Force and potential



On 04/05/2012 01:24 PM, I wrote:

If we choose to use [8] to eliminate dy from [7], we get

-∂U | ∂y |
-dU = ------| ------| dθ [9]
∂y |x ∂θ |r

where both derivatives on the RHS are easy to evaluate
(assuming U contains only gravitational terms).

I forgot to mention that equation [9] is a /vector/ equation.
Both -dU and dθ are vectors. The equation tells us that the
force is in the same direction as dθ ... which makes sense.

As a vector equation, it is valid no matter which (if any)
vector basis you choose to use ... xy, polar, or whatever.
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