For the closed region D, the density formula is F(x, y), and the formula for finding the center of mass: this is the x coordinate for finding the center of mass, and the other coordinate is similar. At the same time, this formula can be extended to the integration of multivariate functions. The principle is still to multiply the required coordinates by the density formula and then divide it by the density formula to do the integration.

When an object has a continuously distributed mass, the vector diameter of the center of mass C is RC =∫ρrdρ/∫ρdρ.

The force on a particle is equal to the vector sum of all external forces acting on the particle system after translation to this point.

It can be inferred from this theorem that:

① The internal force of the particle system cannot affect the movement of the center of mass.

(2) If the main vector of the external force attached to a particle is always zero, its center of mass moves in a straight line at a uniform speed or remains stationary.

(3) If the projection of the main vector of the external force acting on the particle system on a certain axis is always zero, the coordinates of the center of mass on this axis will change at a constant speed or remain unchanged.

I think it is very detailed and my understanding of this formula is much deeper.