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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??:(

9 years ago
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.
9 years ago

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+.......+mn)rc.of mass=(m1r1+m2r2+...............+mnrn)/(m1+m2+............+mn),

m1r1 or m2r2 or mnrn represents the moments of masses m1,m2,mn respectively and rc. of mass is the position vector of centre of mass,all with respect to some common reference point, say ''O''.

HOPE it HELPED YOU.

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9 years ago

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