ﺍﻟﻔﺼل ﺍﻟﺴﺎﺩﺱ :ﺤﺭﻜﺔ ﻤﻨﻅﻭﻤﺔ ﺠﺴﻴﻤﺎﺕ
ﺍﻟﻔﺼﻞ ﺍﻟﺴﺎﺩﺱ
ﺣﺮﻛﺔ ﻣﻨﻈﻮﻣﺔ ﺟﺴﻤﺎﺕ )(Motion of System of Particles
1-6ﺘﻤﻬﻴﺩ :ﻤﺭﻜﺯ ﺍﻟﻜﺘﻠﺔ )(center of mass ﺨﻼل ﺩﺭﺍﺴﺘﻨﺎ ﻟﺤﺭﻜﺔ ﻭﺘﺤﺭﻴﻙ ﺍﻷﺠﺴﺎﻡ ﻟﻡ ﻨﻌﺭ ﺤﺠﻤﻬﺎ ﺃﻭ ﺃﺒﻌﺎﺩﻫﺎ ﺃﻱ ﺍﻫﺘﻤﺎﻡ ،ﻭﺍﻜﺘﻔﻴﻨﺎ ﺒﺘﻤﺜﻴﻠﻬﺎ ﻓﻲ ﺃﻏﻠﺏ ﺍﻷﺤﻴﺎﻥ ﺒﻨﻘﻁﺔ
ﺃﻭ ﺩﺍﺌﺭﺓ ﺼﻐﻴﺭﺓ ﺃﻭ ﻤﺴﺘﻁﻴل .ﻭﺍﻓﺘﺭﻀﻨﺎ ﺃﻥ ﺍﻟﻘﻭﻯ ﺍﻟﻤﺅﺜﺭﺓ ﻋﻠﻰ ﺍﻟﺠﺴﻡ ﺘﻤﺭ ﻜﻠﻬﺎ ﻤﻥ ﻨﻘﻁﺔ ﻭﺍﺤﺩﺓ ﺘﻘﻊ ﻓﻲ ﻤﻨﺘﺼﻔﻪ ،ﻜﻤﺎ
ﺍﻟﺸﻜل )(1-6
ﻓﻲ ﺍﻟﺸﻜل ).(1-6
ﺇﻻ ﺃﻥ ﻫﺫﺍ ﺍﻟﺘﺒﺴﻴﻁ ﻏﻴﺭ ﺼﺤﻴﺢ ﻓﻲ ﻜل ﺍﻷﺤﻭﺍل ﺇﺫ ﻻﻴﻭﺠﺩ ﺠﺴﻡ ﺼﻐﻴﺭ ﻟﺩﺭﺠﺔ ﻴﻤﻜﻥ ﺘﻤﺜﻴﻠﻪ ﺒﻨﻘﻁﺔ ﻭﺍﺤﺩﺓ ،ﻭﻟﻭ ﻨﻅﺭﻨﺎ ﻟﺠﺴﻡ ﻜﺒﻴﺭ ﻴﺘﺤﺭﻙ ﺒﺸﻜل ﺍﻨﺘﻘﺎﻟﻲ )ﺃﻭ ﺍﻨﺴﺤﺎﺒﻲ (translationalﻓﻘﻁ ﻟﻭﺠﺩﻨﺎ ﺃﻥ
ﻜل ﻨﻘﻁﺔ ﻤﻨﻪ ﺘﺘﺤﺭﻙ ﺒﻨﻔﺱ ﺍﻟﺸﻜل ﺘﻤﺎﻤﺎ ،ﻭﺒﺎﻟﺘﺎﻟﻲ ﻓﺈﻥ ﺍﻋﺘﺒﺎﺭ ﻫﺫﺍ ﺍﻟﺠﺴﻡ ﻤﻜﺎﻓﺊ ﻟﻨﻘﻁﺔ ﻭﺍﺤﺩﺓ ﻤﻤﻜﻥ ﻓﻲ ﻫﺫﻩ ﺍﻟﺤﺎﻟﺔ .ﺇﻻ ﺃﻨﻪ ﻟﻭ ﻜﺎﻥ ﻟﺩﻴﻨﺎ ﺠﺴﻡ ﻜﺒﻴﺭ ﻴﺘﺤﺭﻙ
C
ﻋﺸﻭﺍﺌﻴﺎ )ﻜﺎﻨﺘﻘﺎل ﻭﺩﻭﺭﺍﻥ( ﻟﺘﺤﺭﻜﺕ ﻜل ﻨﻘﻁﺔ ﻤﻨﻪ ﺒﺸﻜل ﻤﺨﺘﻠﻑ ﻋﻥ
ﻏﻴﺭﻫﺎ ﻜﺸﺨﺹ ﻴﻘﻔﺯ ﻟﻠﻤﺎﺀ ،ﻜﻤﺎ ﻓﻲ ﺍﻟﺸﻜل ) ،(2-6ﻓﻨﻼﺤﻅ ﺃﻥ ﻜل
ﻨﻘﻁﺔ ﻤﻨﻪ ﺘﺘﺤﺭﻙ ﺒﺸﻜل ﻤﻌﻘﺩ ﺒﺤﻴﺙ ﺘﺩﻭﺭ ﻭﺘﻨﺘﻘل ﺒﻨﻔﺱ ﺍﻟﻭﻗﺕ ﻭﻻﻴﺘﺤﺭﻙ ﻋﻠﻰ ﻤﺴﺎﺭ ﺍﻟﻘﺫﻴﻔﺔ ﺍﻟﻘﻁﻌﻲ ﺍﻟﺫﻱ ﻭﺠﺩﻨﺎﻩ ﻓﻲ ﺍﻟﻔﺼل ﺍﻟﺜﺎﻟﺙ .ﻟﻜﻥ ﻟﻭ ﺃﻤﻌﻨﺎ ﺍﻟﻨﻅﺭ ﻓﻲ ﺍﻟﺸﻜل ) (2-6ﻟﺭﺃﻴﻨﺎ ﻨﻘﻁﺔ ﻤﻌﻴﻨﺔ ﻤﻥ
C
C
C
C
ﺍﻟﺸﻜل )(2-6
155