X represents the coordinate axis; Mi represents the mass of I particles in the material system; Xi represents the coordinates of I particles in the material system.
The center of mass, referred to as the center of mass for short, refers to an imaginary point on the material system where mass is concentrated. Unlike the center of gravity, the center of mass does not have to be in a system with a gravitational field. It is worth noting that unless the gravity field is uniform, the center of mass and the center of gravity of the same material system are usually not on the same imaginary point.
Extended data:
The abbreviation of centroid has nothing to do with the force system acting on the particle system. Let's assume a particle system consisting of n particles, and the mass of each particle is m 1, m2, …, mn. If r 1, r2, ..., rn respectively represent the vector diameter of each particle in the particle system relative to a fixed point, and rc represents the vector diameter of the center of mass, then RC = (m1r1+m2r2+...+mnrn)/(m1+.
When an object has a continuously distributed mass, the vector diameter RC of the center of mass C = ∫ ρ rd ρ/∫ρd ρ, where ρ is the density of the object (or surface or line); Dτ is a volume (or surface, line) element equivalent to ρ; Integral the whole material body (or surface or line) with the distribution density ρ. From Newton's law of motion or momentum theorem of particle system, we can deduce the theorem of motion of the center of mass: the motion of the center of mass is the same as that of a particle located at the center of mass,
The mass of the particle is equal to the total mass of the particle system, and the force on the particle is equal to the vector sum of all external forces 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 on the particle system is always zero, its center of mass will move in a straight line at a uniform speed or remain 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.
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