Centriods
An objects Centriod is simply its center of mass. For example, if you were to put a pin in a 2 dimensional objects center of mass and spin it, it would stay wherever the original energy ended Whereas if you where to spin something on a fulcrum positioned off the objects Centriod, it would stop and then rotate so that the area with the most mass was below the fulcrum
In Symmetrical shapes, the Centriod can be determined by the intersection of the lines of symmetry.
For non-symmetrical shapes, you must split the shape into simple shapes that you can find the centroid of. You must then plug all of the areas, and locations of the individual shapes' centroids into a table and then to an equation.
The Table should be set up like so:
In Symmetrical shapes, the Centriod can be determined by the intersection of the lines of symmetry.
For non-symmetrical shapes, you must split the shape into simple shapes that you can find the centroid of. You must then plug all of the areas, and locations of the individual shapes' centroids into a table and then to an equation.
The Table should be set up like so:
The table
![Picture](/uploads/1/3/7/6/13768163/1721098.jpg?0)
This is basically the way your table needs to be setup before you get into solving the equations.
The number of rows depends on the number of simple shapes you have divided the complex shape into as is illustrated in the photo below.
The number of rows depends on the number of simple shapes you have divided the complex shape into as is illustrated in the photo below.
Solving it
![Picture](/uploads/1/3/7/6/13768163/4627404.jpg?0)
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Ultimately you are solving for X & Y. The locations of the x and y axis, respectively.
The equations for doing so are given in the photo below.
Ultimately you are solving for X & Y. The locations of the x and y axis, respectively.
The equations for doing so are given in the photo below.
Variables
![Picture](/uploads/1/3/7/6/13768163/1353381901.png)
This is false, you should be adding everything from that column together.
Example
The following are photos of the process of finding the centroid of a complex shape.