CM Consider a system comprising two extended bodies, which have masses M1 and M2 and centers of mass at R1 and R2. Prove that the CM of the whole system is at R-MIRI+M2R2 M1M2 (This beautiful result means that in finding the CM of a complicated system, you can treat its components parts just like point masses positioned at their separated centers of mass, even when the component parts are themselves extended bodies.)

Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter9: Dynamics Of A System Of Particles
Section: Chapter Questions
Problem 9.6P
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CM Consider a system comprising two extended bodies, which have masses
M1 and M2 and centers of mass at R1 and R2. Prove that the CM of the whole system
is at
R-MIRI+M2R2
M1M2
(This beautiful result means that in finding the CM of a complicated system, you can
treat its components parts just like point masses positioned at their separated centers
of mass, even when the component parts are themselves extended bodies.)
Transcribed Image Text:CM Consider a system comprising two extended bodies, which have masses M1 and M2 and centers of mass at R1 and R2. Prove that the CM of the whole system is at R-MIRI+M2R2 M1M2 (This beautiful result means that in finding the CM of a complicated system, you can treat its components parts just like point masses positioned at their separated centers of mass, even when the component parts are themselves extended bodies.)
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