Answered: 7 1 1 2 4 4 1 1 3 3 5

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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Question

Introduce an appropriate coordinate system and find the center of mass of the planar lamina. (The answer depends on the position of the coordinate system.)

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Expert Solution

Step 1

Given: Planar lamina

To find: The center of mass by introducing an appropriate coordinate system.

Step 2

Let the coordinate system as-

As seen above the centroid of the first rectangle is $(x_{1}, y_{1}) = (0, \frac{3}{2})$ .
The centroid of the second rectangle is $(x_{2}, y_{2}) = (0, 5)$
The centroid of the third rectangle is $(x_{3}, y_{3}) = (0, \frac{15}{2})$

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