# Statement about torque in a system of particles

• I
• SR_0301
SR_0301
Hello guys, I’m studying Newton’s Mechanics at the first year of engineering, and I would like to ask one question about torque. In my book I found this statement ‘’ Given a system of particles, it’s always possible to determine a pair of forces which torque is indipedent from the pole chosen, and also a force which pass through the pole ( so its torque is 0 respect to that pole ). Unfortunately there aren't examples or a scratch of demonstration of the statement. I think I got the first part about the two forces, but I'm still a bit confused about the true utility. I know the fact that the torque of internal forces which are compatible with Newton third law is zero, and that's practically a consequence of this statement (because the torque is zero indipendently from the pole)

$$\vec \tau = \vec x_1 \times \vec F - \vec x_2 \times \vec F = (\vec x_1 - \vec x_2)\times \vec F$$