Transverse Direction

In the previous chapter, the Curvilinear Motion: Polar Coordinates section developed expressions for acceleration in polar coordinates,

     
where
     
     

Using this representation of acceleration, Newton's Second Law can be expressed in terms of polar coordinates, giving

    ΣF_re_r + ΣF_θe_θ = m (a_re_r + a_θe_θ)

The full relationship is:

Or, each of the two directions can be separated, giving