Lecture Notes 1.2

# Lecture Notes 1.2 - Important concepts from statics Center...

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1 Important concepts from statics – Center of Gravity Real objects are not point- masses, but it is a lot easier to describe them as such. Where should we put the “point”….the center of mass (or gravity) object COM M xdV x = ρ The action of gravity on an object is the same as a single force acting at the COM. If you hang an object by a single point, the COM will always be directly beneath that point. “First moment of mass…or centroid of mass.”

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2 First moments and centroids 4 3 2 ML ydM xdM zdM Mass L ydV xdV zdV Volume L ydA xdA zdA Area L ydL xdL zdL Line Dimensions Q Q Q xz yz xy Δ = = dA ydA dX dX x i i i is axis) - (y plane xz w.r.t. area of Centroid eg Centroid
3 Example: Find C.O.M. of the right half of the homogeneous ellipsoid: x 2 /a 2 + y 2 /b 2 +z 2 /c 2 =1 y x z

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Important concepts from statics – Center of Gravity Can also calculate CG with weighted average approach. = = = + + + + = + + = + + = n i i n i i i cg cg cg W W x x W W W W x W x W x x W W W x M W x W x W x M 1 1 3 2 1 3 2 2 1 1 3 2 1 0 3 3 2 2 1 1 0 ) ( The action of gravity on an object is the same as a single force acting at the COM. If you hang an object by a single point, the COM will always be directly beneath that point. W
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## This note was uploaded on 01/30/2012 for the course 125 208 taught by Professor Shreiber during the Spring '08 term at Rutgers.

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Lecture Notes 1.2 - Important concepts from statics Center...

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