Newton's Third Law (Math)
Name: Paul B.
Has there ever been a mathematical formula produced for Newton's third law -
specifically one that is not merely a demonstration that it works through another physical
system? I know this may sound daft, but I have not been able to find something that
represents this 'law' mathematically, only the linguistic description.
There is, in fact, a simple and yet profound mathematical way to succinctly describe
Newton's third law. Unfortunately, it uses vectors and subscripts, which are difficult
to show in email. However, if we take the F's in the following equation to be vectors,
and the two numbers in brackets separated by commas to be subscripts, we can then write:
F(1,2) = -F(2,1)
In words, the force exerted on object 1 by object 2 is equal in magnitude and opposite in
direction to the force exerted on object 2 by object 1.
Best, Dick Plano
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Update: June 2012