The Centroid of a Planar Region
In this lesson, we learn about the centroid of a planar region and how to calculate moments and centroids. The centroid is a point that acts as the center of the region, and if the region has lines of symmetry, then the centroid is located at their intersection. We also learn about additivity of moments and how to calculate the coordinates of the centroid by dividing the moments by the area. The lesson includes examples of finding the centroid of irregular polygons, strips, and regions between curves.
Calculation of moments and centroids.
Copyright 2005, Department of Mathematics, University of Houston. Created by Selwyn Hollis. Find more information on videos, resources, and lessons at http://online.math.uh.edu/HoustonACT/videocalculus/index.html.
- The Centroid of a Region; Pappus's Theorem on Volume - Practice with The Centroid of a Region; Pappus's Theorem on Volume.
- What is a centroid?
- How do you find the centroid of a shape?
- What is the centroid of a circle, triangle, rectangle, or pentagon?
- What is a moment?
- What is the formula for the moment about the y-axis or x-axis of a region in the plane?
- How do you find the moment of a narrow strip?
- How do you find the moment of the region between two curves?
- How do you find the centroid of the region between two curves?
- How do you find the centroid of the region bounded by y = x and y = x^4?
- How do you find the centroid of the quarter-disk where x^2 + y^2 < R^2?
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Staff Review
The lesson explains how to find the centroid for basic shapes, such as triangles, rectangles, and circles. Then, slightly more complicated shapes are examined. Moments about the axes are also defined, as well as their properties. Some really interesting shapes are used as examples, and the moments of the shape about the axes are used to find the centroid of the shape. Many example shapes that are used are regions between curves.
