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Classical Mechanics | 0th Edition | ISBN: 9781891389221 | Authors: John R Taylor
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Consider a system comprising two extended bodies, which

Chapter 3, Problem 3.20

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QUESTION:

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 + M2 This beautiful result means that in finding the CM of a complicated system, you can treat its component parts just like point masses positioned at their separate centers of mass even when the component parts are themselves extended bodies.

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QUESTION:

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 + M2 This beautiful result means that in finding the CM of a complicated system, you can treat its component parts just like point masses positioned at their separate centers of mass even when the component parts are themselves extended bodies.

ANSWER:

Step 1 of 3

Let us consider a system made of  particles.

The total mass of the system 1 is,

                

Here,  is the mass of the  particle of the system 1.

The total mass of the system 2 is,

                

Here,  is the mass of the  particle of the system 2.

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