Consider a system of 10 (say) point particles each at a fixed distance from each other in 3-D space.
In this case, the number of degrees of freedom: $3*(number-of-particle)-\binom{10}{2}=3*10-45<0$
which is wrong as it cannot be negative.
So, is the number of degrees of freedom 6 by considering it a rigid body?
If yes, why does the above formula fail?
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Hint: you're forgetting about the momentum degrees of freedom. – probably_someone Jun 18 '19 at 13:54
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I do not understand what you mean by momentum degrees of freedom @probably_someone – D.Mason Jun 18 '19 at 13:58
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Possible duplicate of Degree of freedom paradox for a rigid body – Paul Kertscher Jun 18 '19 at 13:58
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Yes, that answered my question @Paul Kertscher – D.Mason Jun 18 '19 at 14:07