One of the toughest challenges for AP Physics C students to get their minds around is that Newton’s Second Law takes so many different forms. There are six separate expressions of Newton’s Second Law of Motion in Calculus-based Intro Physics (a.k.a. AP Physics C Mechanics). Students with some background in physics are accustomed to expressing Newton’s Second Law as F=ma (or Ft=Δp, as is becoming popular with some physics teachers).

However, in AP C, we need both the acceleration and momentum forms of the Second Law, and each takes on three incarnations. In verbal form, here they are:

Single particle, acceleration form

Single particle, momentum form

System of particles, acceleration form

System of particles, momentum form

Angular acceleration form

Angular momentum form

In mathematical form, they look really nice too:

\displaystyle \begin{array}{l}\Sigma \vec{F}={{{\vec{F}}}_{net}}=m\vec{a}\\\\\Sigma \vec{F}={{{\vec{F}}}_{net}}=\frac{d\vec{p}}{dt}\\\\{{{\vec{F}}}_{net,ext}}={{m}_{sys}}{{{\vec{a}}}_{cm}}\\\\{{{\vec{F}}}_{net,ext}}=\frac{d{{{\vec{p}}}_{sys}}}{dt}\text{ (This is the seed equation for conservation of linear momentum}\text{.)}\\\\{{{\vec{\tau }}}_{net}}=I\vec{\alpha }\\\\{{{\vec{\tau }}}_{net,ext}}=\frac{d{{{\vec{l}}}_{sys}}}{dt}\text{ (This is the seed equation for conservation of angular momentum}\text{.)}\end{array}