Question

whats the center of mass

Answer 1

Answer on Question #57741 - Physics - Mechanics - Relativity

Question:

Whats the center of mass

Answer:

The center of mass of a body is weighted with the weight average positions of its mass points. For continuous mass distributions, the local agent of the density is defined as the center of mass. In a homogeneous body agrees with the center of mass with geometric center coincide. The bounceback constitutes an example of a non-homogeneous body.

Center of mass of N material points with masses $m_{i}$ and each radius vector $r_{i}$ is defined as:

$$r_{c} = \frac{1}{M} \sum_{i=0}^{N} m_{i} r_{i} = \frac{\sum_{i=0}^{N} m_{i} r_{i}}{\sum_{i=0}^{N} m_{i}}$$

because mass of N material points with masses $m_{i}$ is the sum of masses all points:

$$M = \sum_{i=0}^{N} m_{i}$$

In the case of a solid body with a density $\rho(r)$:

$$r_{c} = \frac{\int \rho(r) r dV}{\int \rho(r) dV}$$

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