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valocity and acceleration of spherical coordinates and polar coordinates with complete description and derivations?​

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A point P at a time-varying position (r,θ,ϕ) ( r , θ , ϕ ) has position vector ⃗r , velocity ⃗v=˙⃗r v → = r → ˙ , and acceleration ⃗a=¨⃗r a → = r → ¨ given by the following expressions in spherical components.

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