How do you compute the center of gravity (CG) from weight and moment?

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Multiple Choice

How do you compute the center of gravity (CG) from weight and moment?

Explanation:
Center of gravity is the balance point of the weight distribution along the chosen datum. To find it, you take the total moment about that datum and divide by the total weight. The moment for each item is weight times its arm (distance from the datum), and the total moment is the sum of those products. So the formula is CG = Σ(Wi × arm_i) / Σ(Wi). For a quick example: if you have 100 lb at 5 ft and 50 lb at 15 ft, the total moment is 100×5 + 50×15 = 1250 ft-lb, and the total weight is 150 lb. The CG is 1250 / 150 ≈ 8.33 ft from the datum. This method makes sense because CG is effectively a weighted average of the positions, weighted by their weights. Dividing the total moment by the total weight gives a proper distance from the datum, whereas other formulations would not yield a distance (they would have incorrect units or represent just a single item's moment, not the whole distribution).

Center of gravity is the balance point of the weight distribution along the chosen datum. To find it, you take the total moment about that datum and divide by the total weight. The moment for each item is weight times its arm (distance from the datum), and the total moment is the sum of those products. So the formula is CG = Σ(Wi × arm_i) / Σ(Wi).

For a quick example: if you have 100 lb at 5 ft and 50 lb at 15 ft, the total moment is 100×5 + 50×15 = 1250 ft-lb, and the total weight is 150 lb. The CG is 1250 / 150 ≈ 8.33 ft from the datum.

This method makes sense because CG is effectively a weighted average of the positions, weighted by their weights. Dividing the total moment by the total weight gives a proper distance from the datum, whereas other formulations would not yield a distance (they would have incorrect units or represent just a single item's moment, not the whole distribution).

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