explain the point that is Torque at every point is same.
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I believe you are referring to the following: if the nett resultant of a system forces on a body is zero, then we can say that the moment of that system is independent of the point about which the moment is calculated. In symbols, suppose we have a system of forces F⃗ iF→i acting at positions r⃗ ir→i, relative to our co-ordinate origin. The total moment of this system is τ⃗ =∑ir⃗ i×F⃗ iτ→=∑ir→i×F→i.
Now suppose we shift our co-ordinate origin, so that r⃗ i↦r⃗ i+r⃗ r→i↦r→i+r→, for some global displacement r⃗ r→. Then:
τ⃗ ↦∑i(r⃗ +r⃗ i)×F⃗ i=τ⃗ +r⃗ ×∑iF⃗ iτ→↦∑i(r→+r→i)×F→i=τ→+r→×∑iF→i
since ×× distributes over ++. But if the resultant is zero, i.e. ∑iF⃗ i=0∑iF→i=0, then the last term on the right vanishes, and we see that τ⃗ τ→ is unaffected by our shift in origin.
Now suppose we shift our co-ordinate origin, so that r⃗ i↦r⃗ i+r⃗ r→i↦r→i+r→, for some global displacement r⃗ r→. Then:
τ⃗ ↦∑i(r⃗ +r⃗ i)×F⃗ i=τ⃗ +r⃗ ×∑iF⃗ iτ→↦∑i(r→+r→i)×F→i=τ→+r→×∑iF→i
since ×× distributes over ++. But if the resultant is zero, i.e. ∑iF⃗ i=0∑iF→i=0, then the last term on the right vanishes, and we see that τ⃗ τ→ is unaffected by our shift in origin.
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