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Verify that the positions of two particles can be written

Chapter 8, Problem 8.1

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QUESTION:

Verify that the positions of two particles can be written in terms of the CM and relative positions as r1 = R m2r/M and r2 = R m ir/M. Hence confirm that the total KE of the two particles can be expressed as T = 4 MR2 + 4,u,i2, where denotes the reduced mass = m 1m2/ M.

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QUESTION:

Verify that the positions of two particles can be written in terms of the CM and relative positions as r1 = R m2r/M and r2 = R m ir/M. Hence confirm that the total KE of the two particles can be expressed as T = 4 MR2 + 4,u,i2, where denotes the reduced mass = m 1m2/ M.

ANSWER:

Step 1 of 3

Consider the center of mass CM of the two bodies at the position R

Here,

                                                         

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