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Center of Mass

Center of Mass of a body is a unique point where the mass of the body is considered to be concentrated.Center of mass and centre of gravity have some difference between them. Centre of mass concerns with mass and center of gravity concerns with weight. Also centre of mass does not depend on gravitational force while centre of gravity does. 

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 An interesting thing about centre of mass is that it can be located inside the mass or it could be at some point outside the mass. Center of Mass Equation for a system is given by average of mass multiplied by their distances from a reference point. Consider an example of seesaw where it is balanced by a pivot point. Let the two masses on alternate sides be m1 and m2.

Let the distance of these points from a reference point be x1 and x2 respectively then the centre of mass from this point will be:Xc = Center of Mass Formula for Finding Center of Mass of a system of n masses (m1, m2, m3…., mn) is given as: X cm = X1, x2,….x3 are distances of masses from a reference point. X cm is distance of COM (centre of mass) from that reference point. 

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Hence for a system of two mass, center of the mass will be such that it follows following condition: m1 r1 = m2 r2 where r1 and r2 are distance of masses from COM and COM lies on the line which connects the two mass. Above formula can also be written as:x com = for a three dimensional system centre of mass coordinates are given as:x com = , y com = , z com = Above discussion for COM is given for discrete mass. 

For a system with continuous mass distribution, COM is given by the formula: xcom = Center of Mass of a Triangle is same as the centroid of the triangle. Direct method to calculate center of the mass of a triangle whose coordinates are A(x1, x2) , B(x3, x4), C(x5, x6) is to find centroid of triangle using following formula: (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3For a triangle in 3 dimensions COM is given as: COM = (x1 + x2 + x3)/3 , (y1 + y2 + y3)/3, (z1 + z2 + z3)/3