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VectorStaticsLecture18_Chapter9_1_2

# VectorStaticsLecture18_Chapter9_1_2 - Center of Gravity of...

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ME 214 Vector Statics Lecture 18, Chapter 9.1-2 Instructor: A Rezaei Today’s Objectives : Students will: a) understand center of Gravity, Center of mass, and Centroid b) be able to determine the location of these points for a system of particles. The center of gravity (G) is a point which locates the resultant weight of a system of particles or body. the center of mass is a point which locates the resultant mass of a system of particles or body. Generally, its location is the same as that of G. The centroid C is a point which defines the geometric center of an object. Note: The centroid coincides with the center of mass or the center of gravity only if the material of the body has density or specific weight is constant throughout the body (this type of material is called homogenous material). Center of Gravity of system of particles: By replacing the W with a M in these equations, the coordinates of the center of mass can be found.

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Unformatted text preview: Center of Gravity of a Body: STEPS FOR DETERMING AREA CENTROID 1. Choose an appropriate differential element dA at a general point (x,y 2. Express dA in terms of the differentiating element dx (or dy). 3. Determine coordinates (x , y ) of the centroid of the rectangular element in terms of the general point (x,y). 4. Express all the variables and integral limits in the formula using either x or y depending on whether the differential element is in terms of dx or dy, respectively, and integrate. Note: Similar steps are used for determining CG and CM. EXAMPLE 1 Given: The area as shown. Find: The centroid location (x , y) Example 2 Given: The part shown. Find: The centroid of the part. Solution : 1. This body can be divided into the following pieces rectangle (a) + triangle (b) + quarter circular (c) – semicircular area (d) Segment Rectangle Triangle Q. Circle Semi-Circle a b c d...
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VectorStaticsLecture18_Chapter9_1_2 - Center of Gravity of...

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