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CENTROID ,CENTRE OF GRAVITY AND MOMENT OF INERTIA

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UNIT - 4

CENTROID ,CENTRE OF GRAVITY AND MOMENT OF INERTIA

Part-I ( THEORY)

(BT-204) (ENGINEERING MECHANICS)

(Exclusively for A-1 (CS) & A-4 (IT))

Dr.Yogesh Dewang

Associate Professor

Department of Mechanical Engineering

Lakshmi Narain College of Technology, Bhopal

Ph.D. (Mechanical Engineering) (MANIT, Bhopal)

M.Tech (Stress & Vibration Analysis) (MANIT, Bhopal)

B.E. (Mechanical Engineering) (RGPV, Bhopal)

E-Mail Id: yogeshd@lnct.ac.in

Skype Id: yogesh.dewang1

Mobile No: 09179829930

CENTER OF MASS AND CENTER OF GRAVITY

•Consider a uniform rod of length L. When the rod is placed horizontally, each

particle of the rod is pulled by the gravitational force of the earth. The sum of all

three forces will be equal to the total weight of the rod.

•Consider two systems: One is the rod AB of weight W and other is a concentrated

weight W, at a distance 1/3 L from point A.

•These two systems are equivalent as far as the net gravitational pull is concerned, but

the moment of the gravitational forces of the two systems about point A is different.

CENTER OF MASS AND CENTER OF GRAVITY

•If a concentrated weight of Wis put at a distance of 1/2 L from point A, then the

moment of gravitational pull in uniform rod as well as the new system will be same.

•In this case, not only the weight but the first moment of an element of a quantity

about an origin is defined d as the product of its position vector with the element

physical quantity itself.

•With the concept of first moment, we define the centroid centre of mass and centre of

gravity.

CENTER OF MASS AND CENTER OF GRAVITY

CENTER OF GRAVITY AND CENTER OF MASS FOR A SYSTEM OF PARTICLES

DEFINITION OF MOMENTS OF INERTIA FOR AREAS

PARALLEL AXIS THEOREM FOR AN AREA

RADIUS OF GYRATION OF AN AREA

MOMENTS OF INERTIA FOR COMPOSITE AREAS

PRODUCT OF INERTIA FOR AN AREA