Differentiate the position vector twice to obtain the velocity vector and the acceleration vector: r ˙ ˙ = r ˙ ˙ r ^ ^ + r r ^ ^ ˙ ˙ = r ˙ ˙ r ^ ^ + r θ θ ˙ ˙ θ θ ^ ^ , r ¨ ¨ = ( r ¨ ¨ r ^ ^ + r ˙ ˙ r ^ ^ ˙ ˙ ) + ( r ˙ ˙ θ θ ˙ ˙ θ θ ^ ^ + r θ θ ¨ ¨ θ θ ^ ^ + r θ θ ˙ ˙ θ θ ^ ^ ˙ ˙ ) = ( r ¨ ¨ − − r θ θ ˙ ˙ 2 ) r ^ ^ + ( r θ θ ¨ ¨ + 2 r ˙ ˙ θ θ ˙ ˙ ) θ θ ^ ^ .