Moment, Center of Mass, Centroids

Rating:

- (9)
- (1)
- (3)
- (1)
- (2)

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.

(more)

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial

No credit card required

28 Sophia partners guarantee credit transfer.

253 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 22 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

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.

open player in a new window

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).

open player in a new window

Center of Mass, Centroids - Examples

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

open player in a new window

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)