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The vector sum of a system of non-collinear forces acting on a rigid body is given to be non-zero. If the vector sum of all the torques due to the system of forces about a certain point is found to be zero, does this mean that it is necessarily zero about any arbitrary point?

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Best answer

No, it is not necessarily zero

Given :

\(∑_i\vec{F_i}\) ≠ 0

Sum of torque about a certain point A,

\(∑_i\vec{r_i}\times\vec{F_i}\) = 0

Sum of torques about any other point B,

\(∑_i(\vec{r_i-a})\times \vec{F_i}=∑^n_{i=1}\vec{r_i}\times \vec{F_i}-a∑_{i=1}\vec{F_i}\)

So, as a and \(∑^n_{i=1}\vec{F_i}\) are not zero.

torque is not necessarily zero about any other point.

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