Polygon of Forces

Theorem

Let $n$ forces act on a particle where $n \ge 3$.

Let the magnitude and direction of these forces be represented by vectors in space such that the magnitude of the forces is proportional to the length of the vectors.

Then the forces are in equilibrium if and only if the vectors form a polygon.

This is known as a .


Proof


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Also see

  • Definition:Force Polygon


Sources

  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): polygon of forces
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): triangle of forces
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