Determination of center of gravity (centroid) of various objects

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Statement:

Determine center of gravity (centroid) of various objects by analytical solution and experimental observations.

Purpose:

To determine the centroids of various shapes/objects by experimental exercise and compare the same with analytical results.

Apparatus:         

  • Objects of various shapes
  • Plumb bob
  • Graph papers
  • Cutter
  • Meter rod etc.

Related Theory:

Centre of gravity:

“Centre of gravity is a point from which the line of action of resultant of all the gravitational forces passes.”

OR

“It is the point around which the moment of all the gravitational forces completely cancels out each other.”

Centre of mass:

It is the specific point where entire mass of the body is thought to be concentrated.

Centroid:

The geometric centre of the body is called centroid.

Significance of Centroid:
  1. Total resultant gravitational force acts at this point.
  2. Entire mass is supposed to be concentrated at this point.
  3. It is the point at which the body can be supported or stabilized without overturning.

Thus centre of gravity, centre of mass and the centroid, all are physically the same but theoretically different.

Table and Calculations

   Portion           Area    X(mm)   Y(mm)            A.X           A.Y
        1.          
        2.          
        3.          
        Σ          

X=

Y=

 

SHAPES

  CENTRE OF GRAVITY
     EXPERIMENTAL         ANALYTICAL
          X           Y          X          Y
Rectangle        
Triangle        
Circle        
Quarter Circle        

 

Precautions:

  1. Allow the body to become static.
  2. Measure all dimensions precisely.

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