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# Acceleration in Spherical Coordinates

TopAcceleration means change in velocity of body. In words we can say that if there is any change in velocity of body with respect to time then there will be acceleration in that body.
If a body is moving with constant velocity then its acceleration will be equals to 0. Normally the acceleration is given by following formula:
f = d V / d t,
Where 'V' is velocity and 't' is time. Acceleration can be derived in various coordinate systems.
Lets try to derive acceleration in Spherical Coordinates along radial, polar and azimuthal angle direction.

f r = Vr / t + Vr (Vr / ∂ r) + Vθ / r (∂ Vr / ∂ θ) + Vφ / r sin θ (Vr / ∂ φ) – (Vθ2+ Vφ2) / r,

f θ = Vθ / t + Vr (Vθ / ∂ r) + Vθ / r (∂ Vθ / ∂ θ) + Vφ / r sin θ (Vθ / ∂ φ) + (VrVθ) / r – Vφ2 cot θ / r,

f φ = Vφ / t + Vr ( Vφ / ∂ r ) + Vθ / r ( ∂ Vφ / ∂ θ ) + Vφ / r sin θ ( Vφ / ∂ φ ) + ( VrVφ)/ r + (Vφ Vθcot θ) / r,

Here Vr represents velocity component in radial direction.
Vθ represents velocity component in polar anlgle direction and Vφ ­represents velocity component in azimuthal direction.