Statics: Lesson 24 - 3D Moment About a Point and rXF Example

[@mellorine4300]

"Are you scared? Don't be scared. I got you man, I got you." T_T T_T thank you so much professor this really made my day T_T

[@axtror6s228]

+1

[@JoseDuarte-mb5hy]

Thanks so much DR Hanson, I was having trouble understanding this topic. You’re videos really help a lot, they are funny and you are great at explaining.

[@jethior]

the way you teach, your explanation, your joke, your ways of explaining problems, everythingis awesome my dear. you are really true teacher. if it were not for, i donna what to do with mechanics.

[@leonoreellenrose]

you just made the whole topic easier to understand sir... Godbless!

[@georgesadler7830]

DR. Hanson, thank you for another incredible calculation of 3D Moment About a Point and rxF Example.

[@kaili1094]

I am so happy that I can figure this out now. Thank you so much, Professor Hanson.

[@michellelatham3214]

Awesome lesson sir, please keep them coming, they are actually fun to watch!

[@vamp.7233]

Prof. Hanson, you are better than Prof. Michael Seica @the university of Toronto (the #1 rated university in Canada)... congrats!!!

[@godwincornelius201]

Thanks Mr Jeff... All I needed was the definition for "r"

[@ExtraIceGum]

I have a test with one of these problems in 52 minutes. Let my tomb stone read “I tried”

[@filimunisstaff4238]

line my tomb stone right beside yours cause same

[@rnprogamer2522]

When he said i got you homie i knew i was going to understand

[@medicisounds1384]

Hi, in the beginning you said i can take the Point A and attach it to anywhere to the LOA of force. When i do these exact steps using A to E i get completely different Moments. Would it not come out to pretty similar results? I ask that because when you attached it to the point D at first you then had to move the origin? Is that not an extra step that should be eliminated if you just had attached r vector to point E?

[@maxgdh7618]

Asking the same question myself right now, but I just cant figure it out. Did you figure it now, by any chance?

[@laven5583]

I made r vector from point A to point E which gives r vector as rather than the r he used ( ). I get the same answer using either of those r vectors. "Moving the origin" for the force vector just makes it easier to put it in ijk form. Moving the origin is simply just a strategy to make it easier to focus on that vector in the system (expressing the force vector utilizing the entire system is too complicated compared to focusing on a portion of the system because of too many possible unknowns). If we close in on a portion of a system and draw a free body diagram we can solve wherever there are less unknowns to make it easier

[@mushifiqurrahman2630]

@@laven5583 I used but got way different answers, to get the Lambda value i did AD = D - A so - is that correct?

[@mulamulelimanyaga6238]

why is the j hat in the cross product negative .. i thought we were just supposed to add those cross products but im confused that you put a negative on the j hat but + on i and k. can anyone please explain. thank you

[@danielowens6682]

it's basically how the formula works. It has always been i-j+k for cartesian form. We just have to assume that it will be negative for j. I believe everybody was supposed to learn this at the end of Calc ll or at the beginning of Calc lll

[@mulamulelimanyaga6238]

@@danielowens6682 thank you so much

[@gabrialpetersen914]

@@mulamulelimanyaga6238 think of the matrix (called a determinant which is what the cross product is utilizing) as a checkerboard. The signs of the matrix are from something called cofactor expansion so it looks like + - + - but same for the signs below this - + - + but in this case we only had 3 components in our equation hence the + - +. The signs only apply for the rows or columns you are expanding along. In this case we are only expanding along the top row. Technically you could reorder this so the i j k are on the far right column going from top to bottom and same with each vector but the signs would be different because of said cofactor expansion. Look into determinants and cofactors for a more in depth explanation though!

[@angkundiman2492]

Thank you Professor. Glad I found ya

[@NtlakuBaloyi]

You're a life saver👏

[@yashovardhankothari2457]

I love you You are a god You save me from crappy university lectures

[@MichaelOwens433]

Do you need to annotate CW or CCW direction for the moment? If so, can you explain how you determine its direction?

[@mecha_engineer]

No ...the direction is basically the moment in the form of vector

[@princemensah990]

Thank you so much Dr. Hanson for making equilibrium of forces an easy course for me

[@victorcasillas8057]

Why did you use lambda hat for the force vector and not r vector, and how do i know how to tell?

[@papahemmy8587]

Thx, your video helped me test my custom moment program for my ti-84

[@isaacabdella7323]

Let me get that code pls

[@meesh6538]

you save the world thank you

[@skyr6762]

Our savior right here!

[@tataengr9725]

Great video, Jeff!

[@paulferrer2108]

You have to be the best statics professor there is. I wish I was taking your class instead 🥲

[@noahbarrow7979]

why do we need to find the unit vector for DE but not for the position vector?

[@static6107]

In cross products you need to be in Cartesian form. The unit vector let's you break the force into its Cartesian form, the position vector is already in that form so there is no need to find it's unit vector

[@noahbarrow7979]

@@static6107 ahhhhh ha! Thank you!

[@victorcasillas8057]

can you explain that further. Is the magnitude of the r vector 22.7?

[@ElelusivebudgieNor]

My lecturer does the vector cross product a different way. Would there be any reason as to why he would multiply the off-diagonal numbers first and then diagonal numbers . He also doesn't make the outcome of the "j" part of the cross product a negative answer. Would it make sense to do it this way in any scenario or would he be wrong

[@engineeredchannel5649]

Just a different way to do it. I find that method tends to confuse students.

[@ElelusivebudgieNor]

@@engineeredchannel5649 yea I later realised that it gives the same answer and it does indeed confuse students. Not sure why he chose to do it that way

[@youssefelmaghraby6963]

when taking position vector for the force, can i take it from point A (the origin) or do i have to take it from the brggining of the force

[@wadesammohamed]

The question is A positioned in force vector line?

[@nitinpashine]

Doubt about Co-ordinate for pt D. I think that might be (-10, 20,4)

[@anthonylamotta4889]

As always, thank you

[@ireneyhart8717]

Thank you!

[@kininnat3189]

why we need to take D as an origin? why not the same O?

[@naiemataliep9142]

i pray that you win the lotto, thank you

[@jesussaquin6266]

Can the results from the I,j,k components be also considered the individual moments about the x y and z axis?

[@1234jhanson]

Yes indeed!

[@jesussaquin6266]

@@1234jhanson Hey Jeff I just want you to know how much youre helping me in statics, If someday I get the chance of seeing you in person I will buy you a coffee. Stay safe God of statics lol

[@gorchcleave5393]

Shouldn't the unit vector for the force by from point D to point E, and the coordinates of point D are not 0 0 0 but rather something else, -10 20 4?

[@trexinvert]

The unit vector(lambda = normalized position vector..same thing) can be done both ways. What is the unit vector for position vectors: < 1, 1, 1> or ....after you divide each vector by it's magnitude(in math it's called "normalizing" and you can "turn any vector into a unit vector" when you do that) what do you get? Same thing. This is a great observation, because this is a typical "trick exam/quiz problem", where the point coordinates may not all be "given to you" and you need to figure it out. Keep on.

[@daniel533]

if you use D(-10, 20, 4), then you should use E(-14, 32, 7). when you substract D from E the result will be the same

[@victorcasillas8057]

i figured it out. the force vector has a force that has to be taken into account when breaking it up and r vector doesn't.

[@gabrialpetersen914]

Exactly, what youre doing is taking that vector, making it length 1 and stretching it by a factor of 39.The original vector just gives you a direction. So if you take the unit vector it is length one but in the same direction as the original vector. Multiplying by the scalar gives you of course the magnitude or amount of force that is going in that direction.

[@victorcasillas8057]

i take that back. the r vector has to have a magnitude to be a vector. its 22.7 if you take the square root of the square of each component. is that right? so yeah, why don't we also use lambda hat for the position vector.quick please

[@ahmadalsaleh4292]

i diid that

[@justinpratt2545]

could you solve this with the other equation? And if so, how?

[@seedorfo2198]

Can someone explain to me why the vector Force wasn't just -4i + 12j + 3k but rather equals the magnitude × unit vector? 🥺🥺

[@nourrmw2]

It's magnitude multiplied by lambda

[@wadesammohamed]

This really good example

[@evaristogabriel8208]

Thank you........what do we do if the force is in 2d but the rest of the question stays as it is.

[@abdelrahmankhalifa8216]

please specify which plane are working in?

[@firstlegend5105]

@@abdelrahmankhalifa8216 iI don't there's a plane vector in 2d. It just leaves us with x and y axis

[@تويو]

[@Ekkos_Baked]

this guys a walking w

[@tiaanjansevanrensburg143]

Thank you

[@johanjimenez1249]

Thank you master

[@annablue731]

I love you Jeff

[@jesussaquin6266]

Man this guys is saving my ass

[@ilya8132]

I FEEL UNSTOPPABLE

[@waichingwong11]

Nice

[@elsayounes346]

love you

[@rudra1095]

thanks for explaning that annoying R

[@NPT_Legendary_Gaming]

G.O.A.T

[@jdorozco90]

Anyone know why the j-hat cross-product is ‘negative-d’?

[@jdorozco90]

Nvm, cofactor expansion (correct me if I’m off base here)

[@gabrialpetersen914]

@@jdorozco90 That is correct. Think of the matrix as a "checkerboard" + - + - + and same in the downwards direction it has to be the opposite sign next to it.

[@emituntun2460]

Why couldn't it be lamda ED

[@gabrialpetersen914]

It can but it actually works out the same.

[@itziksh3272]

King

[@zachrosedahl2813]

why dont we make a matrix for getting to grandmas house? shouldn't that make the j hat non existent?