- #1
greypilgrim
- 508
- 36
Hi.
I've read the following argument why the torques generated by internal forces add up to zero: Since by Newton's third law all forces come in pairs, so do all internal torques, adding them we get
$$\vec{\tau}_1+\vec{\tau}_2=\vec{r}_1\times\vec{F}_1+\vec{r}_2\times\vec{F}_2=\vec{r}_1\times\vec{F}_1-\vec{r}_2\times\vec{F}_1=(\vec{r}_1-\vec{r}_2)\times\vec{F}_1$$
and apparently this is zero since ##(\vec{r}_1-\vec{r}_2)\parallel\vec{F}_1## .
This argument uses that the forces between two point particles always point towards or away from each other. Is this true in general? I don't quite see why it should be, but I also can't find a counterexample within the fundamental forces (although maybe magnetism, but I don't know how magnetic forces work between point particles).
I've read the following argument why the torques generated by internal forces add up to zero: Since by Newton's third law all forces come in pairs, so do all internal torques, adding them we get
$$\vec{\tau}_1+\vec{\tau}_2=\vec{r}_1\times\vec{F}_1+\vec{r}_2\times\vec{F}_2=\vec{r}_1\times\vec{F}_1-\vec{r}_2\times\vec{F}_1=(\vec{r}_1-\vec{r}_2)\times\vec{F}_1$$
and apparently this is zero since ##(\vec{r}_1-\vec{r}_2)\parallel\vec{F}_1## .
This argument uses that the forces between two point particles always point towards or away from each other. Is this true in general? I don't quite see why it should be, but I also can't find a counterexample within the fundamental forces (although maybe magnetism, but I don't know how magnetic forces work between point particles).