動量守恆律者,物理要論也。其用系算碰撞也。
其義為:使一閉系統毋外力加之,則其動量常數也。若觀乎二物之相撞,則 m1v1+m2v2=m1v1′+m2v2′{\displaystyle m_{1}v_{1}+m_{2}v_{2}=m_{1}v_{1}'+m_{2}v_{2}'} 。 其中 m1{\displaystyle m_{1}} 為物件一之質,m2{\displaystyle m_{2}} 乃物件二之質, v1{\displaystyle v_{1}} 乃物件一之始速, v2{\displaystyle v_{2}} 乃物件二之始速, v1′{\displaystyle v_{1}'} 乃物件一之終速, v2′{\displaystyle v_{2}'} 乃物件二之終速。
證:
∫F1dt=m1v1′−m1v1...(1){\displaystyle \int F_{1}\mathrm {d} t=m_{1}v_{1}'-m_{1}v_{1}...(1)}
∫F2dt=m2v2′−m2v2...(2){\displaystyle \int F_{2}\mathrm {d} t=m_{2}v_{2}'-m_{2}v_{2}...(2)}
以 F1=F2{\displaystyle F_{1}=F_{2}} 之故(見牛頓第三定律),得:
F1=F2{\displaystyle F_{1}=F_{2}}
∫F1dt=∫F2dt{\displaystyle \int F_{1}\mathrm {d} t=\int F_{2}\mathrm {d} t}
(1)=(2){\displaystyle (1)=(2)}
m1v1′−m1v1=m2v2′−m2v2{\displaystyle m_{1}v_{1}'-m_{1}v_{1}=m_{2}v_{2}'-m_{2}v_{2}}
m1v1+m2v2=m1v1′+m2v2′{\displaystyle m_{1}v_{1}+m_{2}v_{2}=m_{1}v_{1}'+m_{2}v_{2}'}