The asking problem:
For the semiannular area, determine the ratio of r1 to r2 for which the centroid of the area is located at
x=-1/2*r2 and y=0.
Note: This problem is a 2D problem and not a 3D. It was taken from the «Distributed forces: Centroids and Centers of Gravity» section of my static course. The files is in word97 format for PC and not for Mac.

So, my question is how can I find this ratio of r1 to r2? I have none idea about that!!

If you will check your answers:
The response is 0.520

First, we need to solve for the x-coordinate of the centroid using the general equation. Then we can equate this with the given x-coordinate of the centroid (-r2/2), and then solve for the ratio r1/r2. See attached for details.

We are given a value of the centroid of -r2/2. We are told to find the ratio of r1/r2 that gives this value of the centroid, so we need an equation for the centroid, that we can equate to the given value. The centroid is a position (x, y). The general equation for an individual coordinate of the centroid of an object is:

where d indicates the integral is over all space, () is the density of the object as a ...

Solution Summary

The semiannual area is examined. The ratio for the centroid of the area is determined.

Using the fact that the centroid of a triangle lies at the intersection of the triangle's medians, which is the point that lies one-third of the way from each side toward the opposite vertex. Find the centroid of the triangle whose vertices are (0,0), (a,0) and (0,b). Assume a > 0 and b >0.

A lamina is described with the help of three curves, given that density of the lamina at a point P is inversely proportional to its distance from y-axis and density at one of the points in the region of the lamina is also given. We need to find the centroid of the region.
For full text of the problem, please find the attachm

Find the centroid of the first octant region that is interior to the to the two cylinders x^2+z^2=1
and Y^2+Z^2=1
centroid for x y and z are
x'=1/M*triple integral of x^2*dV
y'=1/M*triple integral of y^2*dV
z'=1/M*triple integral of z^2*dV

A lamina is described with the help of three curves, given that density of the lamina at a point P is proportional to the square of its distance from x-axis and density at one of the points in the region of the lamina is also given. We need to find the centroid of the region.
For full text of the problem, please find the at

Please help me with the following calculus problems:
1) Set up (do not integrate) an integral for the length of the curve y=tan-1x for x E [0,π).
2) Find the surface area obtained by rotating the curve x=2-y2 around the y axis.
3) Find the centroid of the region bounded by the curve x=2-y2 and the y axis.

The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC. From an arbitrary point O that is not a vertex of triangle ABC, you may take it as a given fact that the location of the centroid of triangle ABC is the vector (vector OA + vector OB + ve

Find the mass and centroid of the plane lamina with the indicated shape and density:
The region bounded by the parabolas y = x^2 and x = y^2, with (x, y) = xy
: is the density symbol

The region in the first quadrant bounded by the graphs of y = x and y = x^2/2 is rotated around the line y=x. Find (a) the centroid of the region and (b) the volume of the solid of revolution.

Sometimes the term centroid throws me for a loop. So, how would I set this problem up?
I'm asked to determine the deflection of the tip of a beam and max direct stress and location for a 2000N load.
Given load=2000N, on the tip of a 1m beam. Beam dimensions are H=80mm B=W=40mm and t=thickness of 1.5mm.