# Assumption on central forces between two particles

## Homework Statement

Consider Newton’s force law for two particles interact through a central force F12(r1',r2',u1,u2), where by Newton’s third law F12 = -F21.

m1(d^2r1/dt^2) = F12(r1,r2,u1,u2)

m2(d^2r2/dt^2) = F21(r1,r2,u1,u2)

A. Show that Newtonian mechanics is form invariant with respect to a Galilean transformation?

## Homework Equations

Newton's third law:
F12 = -F21

Galilean Transform:
t'=t
m'=m
r'=r-vt

## The Attempt at a Solution

I did the A. without a problem. It's the B. that troubles me a bit. I'm sure I'm missing what my prof wants me to find...

I wrote that the forces are equal and have opposite directions. The problem must lie on a single axis since there is only two particles. I'm not sure what other assumption we can make..

Thanks for the help!

Simon Bridge
Homework Helper
When you did part a, you had to make some assumptions.
What were they?

If you did not notice any assumptions, you did not complete part a.
Try going back over your working in more detail... check each step for its reasoning.
Though you may just be expected to list the assumptions for Galilean relativity.

Last edited:
• AllRelative