Center of Gravity of Barycentric Body is Center of Mass

Theorem

Let $B$ be a body in a gravitational field $\mathbf G$ which is non-uniform.

Let $B$ be barycentric.

Then the couple on $B$ induced by $\mathbf G$ is reduced to zero

As a consequence, the center of gravity of $B$ is coincident with the center of mass of $B$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): centre of gravity
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): centre of gravity