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The objective of this video is to find the centroid of a triangle using integration. It has given that the triangle is 4 m in length and 2 m is in height. First of all, the video clears the key step of finding the coordinates of x bar and y bar by deriving equations for f(x) and f(y). Next, the video considers the bottom-left point of the triangle as the reference coordinates and subsequently derives the formula of f(x) in terms of the distance variable x. The video, then, introduces with the integral equation of x bar coordinate and successively expands the equation considering a slice of the triangle.
The equation yields the value of x coordinate and later the video derives the integral equation for y coordinates. At end, the video generalizes the result of triangle centroid concluding the fact that the x coordinate of a centroid of a triangle is located two-third away of its length from the lower corner & the y coordinate of a centroid of a triangle is located one-third away from x axis. Overall, the video tries to give a brief overview on finding centroid coordinates by integration.
Mechanics, the study of forces and physical bodies, underpins a very large proportion of all forms of engineering. A thorough understanding of mechanics is essential to any successful engineer. This course helps develop an understanding of the nature of forces with consideration for how they may be simplified in an engineering context. The conditions of equilibrium are then used to solve a number of problems in 2D and 3D before moving on to a broad range of topics including centroids, distributed loads, friction and virtual work. The course will also provide an introduction to dynamics, with a particular focus on the effects that forces have upon motion.