Question about when calculating the combined vector

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The discussion clarifies that when calculating the combined vector at a point, only the linear forces should be considered, as torque does not affect the resultant force at that specific point. The term "combined vector" refers to the net or resultant force, which is the sum of all forces acting at that location. Torque is calculated separately and does not influence the resultant force since the length is zero at that point. When moments are calculated relative to any point, they can be added to the forces. The conclusion confirms that the resultant force remains unchanged by the moment in this scenario.
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What do you mean by "combined vector"? Do you want to calculate the sum of all forces (I assume they are forces) at that point?
 
I mean "net force" or "resultant force"
 
In that case, the quantity would just as you wrote be given by the linear forces. Torque is given by length times force, and length would be equal to zero for the point you've shown on your picture.
 
So yes, the resultant force remains exactly what you wrote, and the moment does not play a role in it.

Whenever you will calculate a moment relative to any point, you would simply add the moment to it.
 
Thank you! :smile: wasn't sure.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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