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Find the position of center of mass of a system of 3 particles of masses 1kg, 2kg, 3kg that are located at 3 corners of an equilateral triangle of side 1m. Take 1kg mass at the origin and 2kg along x-axis. Find the position of center of mass of a system of 3 particles of masses 1kg, 2kg, 3kg that are located at 3 corners of an equilateral triangle of side 1m. Take 1kg mass at the origin and 2kg along x-axis.
To find the center of mass: Fix one vertex of triangle as origin and give coordinates to other 2 vertices. apply the center of mass formulaA(0, 0) , B (1,0) and C(1/2, sqrt(3)/2)Xcm = M1X1+M2X2+M3X3/(M1+M2+M3) = 1(0)+2(1)+3(1/2)/(1+2+3) = 7/12Ycm = M1Y1+M2Y2+M3Y3/(M1+M2+M3) = 1(0)+2(0)+3(sqrt(3)/2)/(1+2+3) = sqrt(3)/4
To find the center of mass:
A(0, 0) , B (1,0) and C(1/2, sqrt(3)/2)
Xcm = M1X1+M2X2+M3X3/(M1+M2+M3) = 1(0)+2(1)+3(1/2)/(1+2+3) = 7/12
Ycm = M1Y1+M2Y2+M3Y3/(M1+M2+M3) = 1(0)+2(0)+3(sqrt(3)/2)/(1+2+3) = sqrt(3)/4
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