Find the center of mass of a lamina as pictured below, with inner radius 2 and outer radius 4, with densityfunction o(x, y)x² + y?%3D Find the mass of a lamina bounded by y = 2, ĩ, x = 9, and y = 0 with the density functiono(x, y) = x + 3

Answered: Find the center of mass of a lamina as…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Related questions

Question

Find the center of mass of a lamina as pictured below, with inner radius 2 and outer radius 4, with density
function o(x, y)
x² + y?
%3D

Find the mass of a lamina bounded by y = 2, ĩ, x = 9, and y = 0 with the density function
o(x, y) = x + 3

Expert Solution

Step 1

Evaluation of the center of mass of an object with a given density function is an important application of integral calculus. When the density function depends on two variables, the entre of mass can be evaluated using a double integral. When the density function depends on only one variable, it is determined by single-variable integration. The center of mass is expressed as

$x = \frac{M_{y}}{M}, y = \frac{M_{x}}{M}$

Here, $M$ defines the moment, $M_{x}$ defines the moment about the x-axis and $M_{y}$ defines the moment about the y-axis.

We aim to determine the centre of mass of two different lamina with given density functions.