As soon as you said, "What's the weirdest shape you can think of?" Texas was my immediate answer and I laughed so hard when you actually pulled out Texas😄
"Where is the Center of Texas?" This man is asking the real questions. Thanks Jeff, Mercury and Brady are gonna have to thank you for boosting tourism lol. Love the vids keep up the good work!
My professor kept on going back and forth and I got out of the class 2 hours later completely lost. I didn't even get what the hell a centroid is, but you explained it well and thoroughly👏👏👏
Good question. For starters, given a body of a uniform density in a uniform gravitational field, all three of these points are the same point. Center of mass, center of gravity, and centroid. The centroid is purely a geometrical concept, rather than a property of mass distribution. The algorithm for calculating centroids is based on adding up the total moment of either area or volume (i.e. area or volume multiplied by the position vector), and then dividing by the total area or volume. It is a weighted average of the position of every point within a body or section, weighted solely by area or volume. The center of mass is a property of mass distribution, in addition to geometry. This is a weighted average of the positions of all the mass that makes up a body, that considers non-uniform density. If you have a composite material, a heavy part of the composite material can bias the position of the center of mass, but it will leave the centroid unchanged. The center of gravity, not only depends on distribution of mass, but more specifically, on distribution of weight. If you have a body in a non-uniform gravitational field, a stronger part of the gravitational field will bias the position of the center of gravity. It is very rare that we see practical applications of a center of gravity that DOESN'T coincide with the center of mass.
One application where there is a difference between the centroid and the center of gravity, is in the stability of boats. There are three kinds of centers that play a role in the stability of a boat, which are the center of buoyancy, the center of gravity, and the metacenter. I'll leave it to you to look up metacenter, since that isn't the focus of this response. The center of buoyancy occurs at the centroid of the boat's "footprint" in the water. That is, the region of space, where the boat pushes water out of the way, to make way for it to float. This point doesn't care about the distribution of the boat's mass; all it cares about is the geometry of the region of space, where the boat displaces water. The center of gravity of the boat, depends on the boat's distribution of mass. This is why a boat would have a heavy keel on its underside, something that at first sight may seem like excessive weight to drag around. It's to pull the center of mass down, so that it is low enough to keep the boat stable. For a submarine that is completely submerged, the center of gravity has to be below the centroid of its volume. For a surface boat, the metacenter plays a role in the stability as well, which depends on another property of the geometry of the boat's "footprint" in the water.
"Perfectly balanced. As all things should be."
Drinking my Yorkshire Tea Gold as I watch this video
But what did it cost?
@@Hope0fHumanity My brain
As soon as you said, "What's the weirdest shape you can think of?" Texas was my immediate answer and I laughed so hard when you actually pulled out Texas😄
You are the absolute best teacher I have ever seen, Thank you for all the examples, you make understanding Statics so easy!!
"Where is the Center of Texas?" This man is asking the real questions. Thanks Jeff, Mercury and Brady are gonna have to thank you for boosting tourism lol. Love the vids keep up the good work!
Best lecture you can do is to teach other professors to teach like you
My professor kept on going back and forth and I got out of the class 2 hours later completely lost.
I didn't even get what the hell a centroid is, but you explained it well and thoroughly👏👏👏
Nice to see the centroid of Texas. Thank you.
No worries
You are the professor Leonard of Statics
Me frantically hitting subscribe after this comment
God bless you sir. The way you teach, it encourages to learn and study because you make it look easy and fun
Thank you. I am getting ready for the FE exam. Your videos help a lot!!
Absolutely gorgeous the way you found that area's centroid 😊
DR. Hanson, thank you for a great introduction to Centroids/Center of Gravity and also finding the Center of the big State of Texas.
Best doctor ever😂😂😂
I just wanted to thank you for saving me this semester!
I'm from Panama and I really appreciate the way you teach
this guy is the goat
I wish this guy was my prof
man i love you
Thank you
That's exactly what I needed for statics
We don’t have to “love east Texas” per se… but thank you doctor for all of this.
Mercury Texas... That must be where the x bar y bar ranch is...
or is it the x-bar y-bar saloon?
Thank you so much for your videos
I wish you were my professor. :/
thank you for always making things clear for me :')
Best teacher ever
Whatever they are paying you they need to double it. Thank you for the help!
Thank you for being awesome
Thank you, very informative
you are amazing man!
amazing video
អរគុណ
i like it how u trying to reach us
you are amayzing
whoa thats so cool
I wanna know what is that book you were talking about sir. Who's author of that book. What's name of that book
❤
Please, what is the name of the book
which book is that...with tables?
What is the name of the book?
so what is the difference btw centroid and COG when you can balance the body on both of them?
Good question.
For starters, given a body of a uniform density in a uniform gravitational field, all three of these points are the same point. Center of mass, center of gravity, and centroid.
The centroid is purely a geometrical concept, rather than a property of mass distribution. The algorithm for calculating centroids is based on adding up the total moment of either area or volume (i.e. area or volume multiplied by the position vector), and then dividing by the total area or volume. It is a weighted average of the position of every point within a body or section, weighted solely by area or volume.
The center of mass is a property of mass distribution, in addition to geometry. This is a weighted average of the positions of all the mass that makes up a body, that considers non-uniform density. If you have a composite material, a heavy part of the composite material can bias the position of the center of mass, but it will leave the centroid unchanged.
The center of gravity, not only depends on distribution of mass, but more specifically, on distribution of weight. If you have a body in a non-uniform gravitational field, a stronger part of the gravitational field will bias the position of the center of gravity. It is very rare that we see practical applications of a center of gravity that DOESN'T coincide with the center of mass.
One application where there is a difference between the centroid and the center of gravity, is in the stability of boats. There are three kinds of centers that play a role in the stability of a boat, which are the center of buoyancy, the center of gravity, and the metacenter. I'll leave it to you to look up metacenter, since that isn't the focus of this response.
The center of buoyancy occurs at the centroid of the boat's "footprint" in the water. That is, the region of space, where the boat pushes water out of the way, to make way for it to float. This point doesn't care about the distribution of the boat's mass; all it cares about is the geometry of the region of space, where the boat displaces water.
The center of gravity of the boat, depends on the boat's distribution of mass. This is why a boat would have a heavy keel on its underside, something that at first sight may seem like excessive weight to drag around. It's to pull the center of mass down, so that it is low enough to keep the boat stable. For a submarine that is completely submerged, the center of gravity has to be below the centroid of its volume. For a surface boat, the metacenter plays a role in the stability as well, which depends on another property of the geometry of the boat's "footprint" in the water.
What's the title of your book, you refer to that quite frequently. Thanks
just search statics by rc hibbeler
What is the book, if anyone knows..
do you find it?
what is the name of that book?
do you find it?
NOT THE C WORD!
where is the center of CIA
my boring ass* prof could never..
They never do 😂 always youtube rescued me and will try to do so :))
Texas is the greatest country on earth
دكتور مهدي عمك 🤫
اتفق 😂
You are the best