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Verify that the positions of two particles can be written
Chapter 8, Problem 8.1(choose chapter or problem)
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.
Questions & Answers
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,