Net force via center of mass?

J

John W

New member
This is a general physics question. But suppose I have a system of particles, about 30(or n) or so, in 2-dimensional space. If I take one of those particles, I know i can calculate the net force on that particle (lets say the force is gravity between the particles) by using a summation of every other gravitational force on that particle. So if I want to calculate the net force on particle 30, I sum every force that is being exerted on particle 30 by particles 1-29.

But If I calculate the center of mass of these particles, particles 1-29, could I then treat that center of mass as a single particle and use that particle to find the net force on particle 30?

Thanks
 
In general, no.

Imagine a sphere of particles. A particle very near (but not at) the COM experiences very little gravity because most of the particles exactly balance and the net force is nearly zero.

But if you consider everything to be at the COM, calculated force would be intense because none of it would be balanced.

For a spherical object with uniform density (or with each layer being uniformly dense), you can replace the sphere with a point mass at the center for forces acting *outside* the sphere. For general shapes, you cannot do this replacement.
 
Back
Top