Statics: Lesson 22 - 2D Moment About a Point, 2 Methods

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[gabrialpetersen]

At 11:25 you mentioned that if you did the cross product, if you had 5 forces you would have to add all the results from the 5 seperate matrices. Which you can do but to simplify that to one cross product (determinant) there is something called varignons theorem that says that (rxF1)+(rxF2)+...= (rxΣF). This basically means that instead of doing multiple cross products seperately and adding them you can first sum all of the forces and then do the cross product with r and you will get the same answer. By the way your videos are amazing and I really appreciate your hard work on making these, they are the best on youtube!

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[georgesadler]

DR. Hanson, this is a fantastic demonstration of 2D Moments about a Point using two powerful Methods. As always I appreciate your help and encouragement.

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[ambrose_]

Another way of applying Method 2 (and arguably simpler), is to extend the force line backwards past point A and then draw a perpendicular line from point A to the extended force line (this will be the d that you want to find in the formula M = F*d). That will form a right trangle. Since you know 45 degrees is one of the angles, you can find that sin(45)*3m= the perpendicular length. Now you plug that into M = F*d and you have your solution.

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[yasinozkan]

Thanks for the videos sir.
We could also use the M=Fd by again sliding the force through line of action and use at the center right? It is faster as well.

[ilya]

One thing I'm a little confused about for this one is how the motion is taking place. Is the rod a semicircle that's being pulled 'out' of some surface by its end? I understand the math part, but if this were described to me in words I'm now sure I'd be able to visualize it.

[louislaplante]

You could also use Law of Transmissibility to have 500 * 2.12 to get 1060

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[xg]

I don't get where 2.12 came from. Wouldn't the length from the center to the line of action be 3.?

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[sebastiancurry]

where did the 5.12 come from? Wouldnt the distance in the x for that Y force be 4.28 cause the r2 vector has a hypotenuse of 3, so the X on that side would also be 2.12?