Expression for the acceleration of a particle in polar coordinates
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In two dimensional polar rθ coordinates, the force and acceleration vectors are F = Frer + Fθeθ and a = arer + aθeθ. Thus, in component form, we have, Fr = mar = m (r − rθ˙2) Fθ = maθ = m (rθ ¨+2˙rθ˙) . Polar coordinates can be extended to three dimensions in a very straightforward manner.
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