Calculate The Centroid Or Center Of Mass Of A Region
In these lessons, we will look at how to calculate the centroid or the center of mass of a region.
Related Pages
Centroid Of A Triangle
More Calculus Lessons
Looking for some Calculus help? We have a a series of free calculus videos that will explain the various concepts of calculus.
Formulas To Find The Moments And Center Of Mass Of A Region
The following table gives the formulas for the moments and center of mass of a region. Scroll down the page for examples and solutions on how to use the formulas for different applications.
Find The Centroid Of A Triangular Region On The Coordinate Plane
How to determine the centroid of a triangular region with uniform density?
Example:
Find the centroid of the triangle with vertices (0,0), (3,0), (0,5).
Find The Centroid Of A Bounded Region Involving Two Quadratic Functions
How to determine the centroid of a region bounded by two quadratic functions with uniform density?
Example:
Find the centroid of the region with uniform density bounded by the graphs of the functions
f(x) = x2 + 4 and g(x) = 2x2.
How To Find The Center Of Mass Of A Region Using Calculus?
Centroids / Centers of Mass - Part 1 of 2
This video will give the formula and calculate part 1 of an example.
Example:
Find centroid of region bonded by the two curves, y = x2 and y = 8 - x2
Centroids / Centers of Mass - Part 2 of 2
This video gives part 2 of the problem of finding the centroids of a region.
How To Find The Center Of Mass Of A Thin Plate Using Calculus?
Center of Mass / Centroid, Example 1, Part 1
Find the center of mass of the indicated region.
Center of Mass / Centroid, Example 1, Part 2
We continue with part 2 of finding the center of mass of a thin plate using calculus.
How To Use Integration To Find Moments And Center Of Mass Of A Thin Plate?
Moments and Center of Mass - Part 1
Moments and Center of Mass - Part 2
Calculating the moments and center of mass of a thin plate with integration.
Center Of Mass Of A Thin Plate
Example:
Find the center of mass of a thin plate covering the region bounded above by the parabola
y = 4 - x2 and below by the x-axis. Assume the density of the plate at the
point (x,y) is δ = 2x2, which is twice the square of the distance from
the point to the y-axis.
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