"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!
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😄
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👏👏👏
Prof Jeff you are amazing the way you expl that s.f. by V. Symbol correlating to tha still scissors when expanded scissors shear away an object this tells your genious
Looked through so many posts just to com to your video to figure out where my textbook was getting the y-bar for a triangle from. Thank you for explaining the importance of the chart.
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.
