تکانه - ویکی‌پدیا، دانشنامهٔ آزاد

${\displaystyle {\vec {p}}=m{\vec {v}}}$

${\displaystyle d{\vec {p}}={F}.d{t}}$

${\displaystyle {F}={d{\vec {p}} \over d{t}}}$

${\displaystyle {\vec {p}}=m{\vec {v}}}$

${\displaystyle {F}={m.d{\vec {v}} \over d{t}}}$

${\displaystyle {a}={d{\vec {v}} \over d{t}}}$

${\displaystyle {F}={m}.{a}}$

${\displaystyle \mathbf {P} =\sum _{i=1}^{N}\mathbf {p} _{i}=\mathbf {p} _{1}+\mathbf {p} _{2}+\cdots +\mathbf {p} _{N}=m_{1}\mathbf {v} _{1}+m_{2}\mathbf {v} _{2}+\cdots +m_{N}\mathbf {v} _{N}\,\!}$

${\displaystyle M\mathbf {r} _{cm}=\sum _{i=1}^{N}m_{i}\mathbf {r} _{i}=m_{1}\mathbf {r} _{1}+m_{2}\mathbf {r} _{2}+\cdots +m_{N}\mathbf {r} _{N}\,\!}$

${\displaystyle M=\sum _{i=1}^{N}m_{i}=m_{1}+m_{2}+\cdots +m_{N}\,\!}$

${\displaystyle M\mathbf {V} _{cm}=\sum _{i=1}^{N}m_{i}\mathbf {v} _{i}=m_{1}\mathbf {v} _{1}+m_{2}\mathbf {v} _{2}+\cdots +m_{N}\mathbf {v} _{N}\,\!}$

${\displaystyle \mathbf {P} =\mathbf {P} _{cm}=M\mathbf {V} _{cm}\,\!}$

${\displaystyle \mathbf {F} ={\mathrm {d} \mathbf {P} \over \mathrm {d} t}={\mathrm {d} \mathbf {P} _{cm} \over \mathrm {d} t}\,\!}$

${\displaystyle \mathbf {f} _{i}=\mathbf {f} _{i}^{ext}+(\mathbf {f} _{1\rightarrow i}^{int}+\mathbf {f} _{2\rightarrow i}^{int}+\cdots +\mathbf {f} _{(i-1)\rightarrow i}^{int}+\mathbf {f} _{(i+1)\rightarrow i}^{int}+\cdots +\mathbf {f} _{N\rightarrow i}^{int})\,\!}$

${\displaystyle \mathbf {F} =\mathbf {F} _{ext}=\sum _{i=1}^{N}\mathbf {f} _{i}^{ext}=\mathbf {f} _{1}^{ext}+\mathbf {f} _{2}^{ext}+\cdots +\mathbf {f} _{N}^{ext}\,\!}$

${\displaystyle \mathbf {F} _{ext}={\mathrm {d} \mathbf {P} \over \mathrm {d} t}={\mathrm {d} \mathbf {P} _{cm} \over \mathrm {d} t}\,\!}$

${\displaystyle \mathbf {F} _{ext}=0\Rightarrow {\mathrm {d} \mathbf {P} \over \mathrm {d} t}=0\Rightarrow \mathbf {P} =Const.\,\!}$

${\displaystyle \mathbf {F} _{ext}=F_{x}\mathbf {i} +F_{y}\mathbf {j} +F_{z}\mathbf {k} \qquad \mathbf {P} =P_{x}\mathbf {i} +P_{y}\mathbf {j} +P_{z}\mathbf {k} \,\!}$

${\displaystyle \Delta \mathbf {p} _{1}+\Delta \mathbf {p} _{2}=0\quad \Rightarrow \quad \Delta \mathbf {p} _{1}=-\Delta \mathbf {p} _{2}\,\!}$

${\displaystyle 0=m\mathbf {v} +M\mathbf {V} \quad \Rightarrow \quad \mathbf {V} =-{m \over M}\mathbf {v} \,\!}$