A point may be found out in a body, through which the resultant of all such parallel forces act. The point, through which the whole weight of the body acts is known as Center of Gravity (Briefly C.G). Each body has only one CG and its location in the body is depends upon the shape of the body.
We can find the center of gravity or centroid by the following methods.
- By Geometrical consideration
- By Moment
- By Graphical Method
Centroid: Any plane figures don’t have mass. it only has area. Center of the plane figure is known as centroid. You have understood the difference between C.G and Centroid.
Axis of Reference: Center of Gravity of a body always calculated with reference to some axis. For plane figure we can assume axis are X-X and Y-Y, in this case the C.G of the Axis X-X is x and along Y-Y axis y.
By Geometrical Consideration:
1. We can find the C.G point in a rectangle and square where two diagonal intersect each other.
Reference to Fig. 4.1 Rectangle AC and BD intersecting each other at point O. Point O is the C.G of the figure, we can locate the C.G point from base BC at AB/2 or DC/2. Similarly, from base DC location of the C.G will be at BC/2 or AD/2.
2. We can find the C.G point in a Triangle where three median intersects each other.
Reference to Fig. 4.1 Equilateral triangle ABC has three medians from vertex A, C and B intersecting each other at point O. Hence, point O is the C.G of the figure, we can locate the C.G point from base AB at height of triangle(H)/2. The system of finding the C.G of the other Triangle will remain same, but the calculation will change depend on the Triangle.
3. We can find the C.G point in a Trapezium ABCD at the height of the figure.
Reference to Fig. 4.1 Trapezium ABCD has a height, it is the shortest distance between the two sides AB and CD. The location of the C.G will be at H(AB+2CD)/3(AB+CD)
By Moment:
An object has a body mass M, now we need to find out its Center of Gravity. Let’s assume (Ref. Fig. 4.4) there are 2 different point has mass M1 and M2 at a distance from the C.G line X1 and X2 respectively.
Center of Gravity of Plane Figures
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