Undergrad Why if net force=zero, moment at any point is same?

[gen x]

Why as long net force= zero, moment at any point is the same but if net force= non zero, that is not case anymore?

Here is simple example:

Net force=zero case: F1=10, F2=40, N=50

Moment at A= +20Nm

Moment at B=+20Nm

Any point you choose you will get same moment..

Net force = non zero: F1=10, F2=40, N=30

Moment at A=+20Nm

Moment at B=+100Nm

Now, moment is not the same in every point.

 

[Baluncore]

Please show the equations that you use to compute the moments, for the cases you present.

 

[A.T.]

Why as long net force= zero, moment at any point is the same but if net force= non zero, that is not case anymore?

If $\vec{F_{net}}$ is the net force, and $\vec{M_{net,a}}$ is the net moment around the point $\vec{a}$, then the net moment around any point $\vec{b}$ is given by:
$$\vec{M_{net,b}} = \vec{M_{net,a}} + (\vec{a} - \vec{b}) \times \vec{F_{net}}$$
Which for $\vec{F_{net}}=0$ simplifies to:
$$\vec{M_{net,b}} = \vec{M_{net,a}}$$

 

[gen x]

Please show the equations that you use to compute the moments, for the cases you present.

Net force=zero case: F1=10, F2=40, N=50

Moment at A=-10x2+40x1=+20Nm

Moment at B= 10x2-50x4+40x5=+20Nm



Net force = non zero: F1=10, F2=40, N=30

Moment at A=-10x2+40x1 =+20Nm

Moment at B= 10x2-30x4+40x5 =+100Nm

$$\vec{M_{net,b}} = \vec{M_{net,a}} + (\vec{a} - \vec{b}) \times \vec{F_{net}}$$

How do you get this equation?

 

[Hill]

$\vec{F}\times(\vec{a}+\vec{b})=\vec{F}\times\vec{a}+\vec{F}\times\vec{b}$

 

[A.T.]

How do you get this equation?

This is basic transfer of moments to another reference point:

 

[gen x]

This is basic transfer of moments to another reference point:

Why is vector r a/p (lever arm) not perpendicular to force F?
moment of point P must be: Mp= lever arm perpendicular to force F x force F

 

[A.T.]

Why is vector r a/p (lever arm) not perpendicular to force F?
moment of point P must be: Mp= lever arm perpendicular to force F x force F

https://en.wikipedia.org/wiki/Cross_product