Centre of Mass of Rigid Bodies
For continuous distribution of mass, the summation in the formula of CM should be replaced by integration.
`vecr_(CM)= (intdmvecr)/(intdm)= 1/M intdmvecr`
Where `dm` is elementary mass, `vecr` is position vector of its `CM` and `M` is total mass.
If `x, y, z` are the co-ordinates of the elementary mass `dm`, then co-ordinates of `CM` of the object are given by
`vecX_(CM)= (intxdm)/(intdm)= (intxdm)/M`
`vecY_(CM)= (intydm)/(intdm) = (intydm)/M`
`vecZ_(CM)= (intzdm)/(intdm)= (intzdm)/M`
`vecr_(CM)= (intdmvecr)/(intdm)= 1/M intdmvecr`
Where `dm` is elementary mass, `vecr` is position vector of its `CM` and `M` is total mass.
If `x, y, z` are the co-ordinates of the elementary mass `dm`, then co-ordinates of `CM` of the object are given by
`vecX_(CM)= (intxdm)/(intdm)= (intxdm)/M`
`vecY_(CM)= (intydm)/(intdm) = (intydm)/M`
`vecZ_(CM)= (intzdm)/(intdm)= (intzdm)/M`