Apply the center of mass equation to a system of up to 8 point masses. Drag the masses on a coordinate plane and see the weighted-average ledger, the running sums, and the center of mass worked out step by step.
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The Center of Mass Diagram Builder works the center of mass equation for a system of up to eight point masses in two dimensions. Enter or drag each mass on the coordinate plane and the diagram sizes every dot in proportion to its mass, draws the weighted-average connectors, and marks the center of mass with a crosshair.
The contribution ledger shows every m·x and m·y term, the running sums, each mass fraction, and the final division x_cm = Σm·x / M and y_cm = Σm·y / M — the same worked construction AP Physics 1 expects for systems of particles.
For a system of point masses, x_cm = (Σ m_i x_i) / (Σ m_i) and y_cm = (Σ m_i y_i) / (Σ m_i). Each coordinate is weighted by its mass, so the center of mass shifts toward the heavier masses.
No. The center of mass is a weighted average, so it is unit-invariant. Using grams instead of kilograms changes the ledger labels but never the coordinates.
Yes. The center of mass always lies inside the convex hull of the point masses, but it need not coincide with any of them — an L-shaped or ring-shaped system puts it in empty space.
The mass weighting cancels and the center of mass becomes the plain average of the positions, which is the geometric centroid of the points.
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