The center of gravity represents the average location of an object or system's mass distribution. For simple shapes it lies at the geometric center. For irregular bodies, finding the exact center of gravity position requires calculations.
Key properties:
- Represents the concentrated point where weight acts
- Object rotates around the center of gravity if unconstrained
- Net external forces act through this point
Calculating the center of gravity
Mathematically, the center of gravity is the weighted average location of differential mass elements: center of gravity = Σ(dm * r) / Σdm Where: dm = differential mass element r = position vector from origin to dm For a 1D body this reduces to: center of gravity = Σ(x * m) / Σm Where x = distance of each mass m from the origin. For 2D or 3D bodies, y- and z-coordinates are incorporated. Complex shapes require integration.Locating the center of gravity
Regular objects have centralized center of gravity s. Irregular bodies require:- Separating into geometric primitives with known center of gravity s
- Determining the center of gravity of each sub-shape
- Combining the center of gravity s based on a weighted average
- Center of gravity lies along the vertical axis line through the combined center of gravity s
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