Guys,I dont seem to understand how the general equation for Centre of mass was derived.I mean,yeah,i get that in a rod,or other symmetric structures,it should lie at the point of symmetry more or less,How waz the general equation derived?m1r1+m2r2+m3r3+....mn rn/m1+m2+m3...etc??..What does the term M1r1 actually mean??:(

Centre of mass of a system actually lies on that particular line which divides the system momenta wise into 2 equal portions.That line is called line of symmetry.If a system has more than 1 line of symmetry,then C.M of system will lie on the intersection of lines of symmetry.Here momenta(M.Rcm) is a vector quantity and the net momenta of system is the summation of momenta of every individual particle of system.From this the main equation of C.M is derived. Here,M=total mass of system, Rcm =Position vector of C.M of the system w.r.t origin depending upon consideration. m1,m2,m3.... = mass of individual particles of system. Please approve if you like.

dear friend,

centre of mass of a rigid body is the point at which the sum of the moment of mass of all the particles becomes zero. so,in the formula

(m₁+m₂+.......+m_n)r_{c.of mass}=(m₁r₁+m₂r₂+...............+m_nr_n)/(m₁+m₂+............+m_n),

 m₁r₁ or m₂r₂ or m_nr_n represents the moments of masses m₁,m₂,m_n respectively and r_{c. of mass} is the position vector of centre of mass,all with respect to some common reference point, say ''O''.

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if u read resnik haliday u can understand beter

 

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consider an coordinate axis containing points p(X1,Y1) , Q(X2,Y2) , R(X3,Y3) .  those points are the location of three objects of mass M1,M2,M3 respectively. then the X coordinate of the center of mass [C.O.M] of the whole system would be Xc.o.m= (M1X1+M2X2+M3X3)/M1+M2+M3 and similarly the y coordinate of c.o.m would be Yc.o.m= (M1Y1+M2Y2+M3Y3)/M1+M2+M3                 hope u got your answer

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