Home > Courses > 1P21_Sternin > LinearAngularMomentum Linear Momentum Momentum $\vec{p} = m \vec{V}$, in kg.m/s Rewrite N2L as $\vec{F} = \lim_{\Delta t \rightarrow 0} {{\Delta \vec{p}}\over{\Delta t}} \quad \mbox{or} \quad \sum \vec{F}_{\rm ext} = \lim_{\Delta t \rightarrow 0} {{\Delta \vec{p}_{\rm total}}\over{\Delta t}}$ Total impulse ${\cal I} = F \, \Delta t = \Delta p = \Delta (mV)$ is the area under the curve on the $F$ vs. $t$ graph N2L as the law of conservation of momentum $\sum \vec{F}_{\rm ext}=0 \quad \rightarrow \quad \Delta \vec{p}_{\rm total} = 0 \quad \rightarrow \quad \vec{p}_{\rm total} ={\rm const}$ Conservation Laws in solving problems Elastic collision C.o.M. and C.o.K.E. \begin{eqnarray*} \vec{V}_{f,1} & = & {\frac{m_1 - m_2}{m_1 + m_2}} \, \vec{V}_{i,1} \quad + \quad \frac{2m_2}{m_1 + m_2} \, \vec{V}_{i,2} \\ \vec{V}_{f,2} & = & {\frac{2m_1}{m_1 + m_2}} \, \vec{V}_{i,1} \quad + \quad \frac{m_2 - m_1}{m_1 + m_2} \, \vec{V}_{i,2} \end{eqnarray*} Inelastic collision $\Delta E\neq0$, but C.o.M. holds! $\vec{V}_f \quad = \quad {{m_1}\over{m_1 + m_2}} \, \vec{V}_{i,1} \quad + \quad {{m_2}\over{m_1 + m_2}} \, \vec{V}_{i,2}$