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

AI Thread Summary
To find the center of mass (CM) in a 3D coordinate system, use the formula [sigma miri]/total mass for discrete particles, where mi is the mass and ri is the position vector. For continuous distributions, the CM is calculated using the triple integral [r*rho(r)dV]/total mass, with rho(r) representing the density at position r. The position vector r is defined in Cartesian coordinates as r = xi + yj + zk, where (x, y, z) are the coordinates of the point. This method applies universally, not just in Cartesian coordinates. Understanding these calculations is essential for accurately determining the center of mass in various applications.
smriti
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hi,
Can anyone please help me to find the centre of mass of an object in a 3D co-ordinate system.
Thanks in advance
 
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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.
 
Last edited:
can u please wht does the r stands for?
 
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.
 

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