Where can I find the centre of mass in a 3D co-ordinate system?

[smriti]

hi,
Can anyone please help me to find the centre of mass of an object in a 3D co-ordinate system.
Thanks in advance

 

[Shooting Star]

In cartesian co-ordinates, the CM of of a system of particles is [sigma miri]/total mass. Simply put, multiply the mass at a point by its posn vector, add all of these, and divide by the total mass.

If it's a continuous distribution, it will become triple integral [r*rho(r)dV]/total mass, where rho(r) is the density at r.

EDIT: This is the general form, not limited to Cartesian co-ordinates.

 

[smriti]

can u please wht does the r stands for?

 

[Shooting Star]

r denotes the position vector of a point wrt the origin. For example, if the Cartesian co-ordinates of a point is (x,y,z), then r = xi + yj + zk.