Moment, Center of Mass, Centroids

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Description:

The student should be able to calculate the center of mass of linear and two-dimensional systems of discrete point masses, and apply integrals to finding the center of mass of a planar lamina.

This packet consists of 3 videos and a problem set. The first video shows how to calculate center of mass for linear and two-dimensional systems of discrete masses. The second develops the use of integration to find the center of mass of a planar lamina, and with that, the centroid of a region. The third video walks through some examples.

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Tutorial

Prerequisites

Students should be able to apply the concept of integration as a summation.

Moments and Center of Mass - One and Two Dimensional Discrete Mass Systems

This video looks at the terminology and techniques involved with finding center of mass of linear and two-dimensional systems.

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Center of Mass - Planar Laminas

This video develops the integral technique for calculating the center of mass of a planar lamina (and centroid of a region).

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Center of Mass, Centroids - Examples

This video walks through three example of applications of the formulas.

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Problem Set

1. Find the center of mass of the given point masses lying on the x-axis

$m subscript 1 equals 7 comma space m subscript 2 equals 4 comma space m subscript 3 equals 3 comma space m subscript 4 equals 8 x subscript 1 equals negative 3 comma space x subscript 2 equals negative 2 comma space x subscript 3 equals 5 comma space x subscript 4 equals 9$ (2.636)

2. Find the center of mass of the given system of point masses

$m colon space space space space space space space space space space space space 4 space space space space space space space space space space space 2 space space space space space space space space space 3.5 space space space space space space space space space 6 left parenthesis x subscript i comma y subscript i right parenthesis colon space space space space left parenthesis 2 comma 3 right parenthesis space space space space left parenthesis negative 1 comma 5 right parenthesis space space space space left parenthesis 6 comma 8 right parenthesis space space space space left parenthesis negative 3 comma 0 right parenthesis$ (0.581, 3.226)