Newton’s second law

  • When a body experiences a net force Fnet, its momentum p = mv changes.
  • The rate of change of momentum is directly proportional to Fnet.
  • If SI units are used,

\begin{aligned}{{F}_{net}}=\frac{dp}{dt}\end{aligned}

  • For a body with constant mass m, the second law is reduced to Fnet = ma.

\begin{aligned}{{F}_{net}}&=\frac{d(mv)}{dt}\\&=m\frac{dv}{dt}\\&=ma\end{aligned}

  • For a body with “changing” mass but “constant” v, the second law is reduced to Fnet = vdm/dt

\begin{aligned}{{F}_{net}}&=\frac{d(mv)}{dt}\\&=v\frac{dm}{dt}\end{aligned}

  • Integrating both sides of the equation leads to the concept of impulse.

\displaystyle \text{Imp}={{F}_{net}}\Delta t=\Delta p

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