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Concepts in Thermal Physics$

Stephen J. Blundell and Katherine M. Blundell

Print publication date: 2009

Print ISBN-13: 9780199562091

Published to Oxford Scholarship Online: February 2010

DOI: 10.1093/acprof:oso/9780199562091.001.0001

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(p.482) G Reduced mass

(p.482) G Reduced mass

Source:
Concepts in Thermal Physics
Publisher:
Oxford University Press

Consider two particles with masses m 1 and m 2 located at positions r1 and r2 and held together by a force F(r) that depends only on the distance r = |r| = |r1r2| (see Fig. G.1).

G Reduced mass

Fig. G.1 The forces exerted by two particles on one another.

Thus we have
m 1 r ¨ 1 = F ( r ) ,
(G.1)
m 2 r ¨ 2 = F ( r ) ,
(G.2)
and hence
r ¨ = ( m 1 1 + m 2 1 ) F ( r ) ,
(G.4)
which can be written
μ r ¨ = F ( r ) ,
(G.5)
where μ is the reduced mass given by
1 μ = 1 m 1 + 1 m 2 ,
(G.6)
or equivalently
μ = m 1 m 2 m 1 + m 2 .
(G.7)