Normal Direction

Tangent Direction

Previously, in the Curvilinear Motion: Normal/Tangential Coordinates section in chapter 1, equations for the normal and tangential components of acceleration were derived for a particle moving in a plane curved path. These were,

     a_t = dv/dt              a_n = v²/ρ

Newton's Second Law can also be expressed in terms of normal and tangential coordinates,

    ΣF_te_t + ΣF_ne_n = m (a_te_t + a_ne_n )

Substituting gives,

     ΣF_te_t + ΣF_ne_n = m (dv/dte_t + v²/ρe_n )

Or for just the tangent direction,

     ΣF_t = m dv/dt  

In the normal direction,

     ΣF_n = m v²/ρ