Chpater 9-Center of Gravity and Centroid

# Chpater 9-Center of Gravity and Centroid - C Centre of...

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Centre of Gravity and Centroid Lectures 15-16 (Chapter 9) Dr. Marina Milner-Bolotin [email protected] Check Blackboard for course web site! C ·

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Part I: Lecture 15 – Centre of Gravity, Centre of Mass and Centroid of a Body Goals: To understand the concepts of center of gravity, center of mass, and centroid. b) To be able to determine the location of these points for a system of particles or a rigid body. 2 One concern about a sport utility vehicle (SUVs) is that it might tip over while taking a sharp turn. One of the important factors in determining its stability is the SUV’s center of mass . Should it be higher or lower for making a SUV more stable? How do you determine its location?
A Particle versus a Mechanical System A particle is: A body whose physical dimensions are so small compared with the distances involved that we can treat the body as a point. A mechanical system is: 1. A system of particles collection of atoms in a container 2. A continuous object a gymnast leaping through the air a ball tossed into the air 3. A collection of continuous objects all the loads on a structure Earth-Moon system

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Concept of Centroid 4 The centroid C is a point which defines the geometric center of an object. The centroid coincides with the center of mass or the center of gravity only if the material of the body is homogenous (density or specific weight is constant throughout the body). If an object has an axis of symmetry, then the centroid of an object lies on that axis. In some cases, the centroid is not located on the object. For example think of a bagel.
Centre of Mass and Centre of Gravity 5 Definition of center of mass (C.M.) When external forces are applied to a body, this body moves as if acted by a single force (net force); the point of application of this force, is called the CENTER OF MASS. Definition of center of gravity The earth exerts a force on each tiny element of mass in a body. The resultant of all these forces is what we call WEIGHT. The point of application of the weight is called the CENTER OF GRAVITY. Center of mass or center of gravity may not exist inside the body.

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How Do We Find C.M.? 6 1. If the body is a single particle, its C.M. coincides with the particle’s position. 2. If the body is made of two single particles, the coordinates of the C.M. are a function of the coordinates of the particles and their masses. + + = + + = 2 1 2 2 1 1 2 1 2 2 1 1 m m m y m y y m m m x m x x cm cm The coordinates of the C.M. are given with respect to the same frame of reference as the coordinates of the individual particles. y 2 x 1 m 1 x 2 y 1 m 2
How Do We Find C.M.? 7 3. If the body is made of n single particles ? In that case, the C.M. is a function of the positions of the particles and their masses

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## This note was uploaded on 05/23/2010 for the course PHYSICS PCS211 taught by Professor Juan during the Winter '09 term at Ryerson.

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Chpater 9-Center of Gravity and Centroid - C Centre of...

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