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Moment as a cross product

The moment of a force about a point can be found using vectors in the plane, without measuring angles directly. It is the zz-component of the cross product between the arm vector and the force.

M=rxFy−ryFxM = r_xF_y - r_yF_xmoment about O, r⃗\vec r is the vector from O to the point of application

Symbols

r⃗\vec rvector from the point to the point of application
F⃗\vec FforceN

Example

r⃗=(0.3,0)\vec r=(0.3,0) m and F⃗=(0,50)\vec F=(0,50) N: M=0.3⋅50−0⋅0=15M = 0.3\cdot50 - 0\cdot0 = 15 Nm.

A positive sign means the moment is counterclockwise, a negative sign clockwise.
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Part of Foundations of Mathematics: Vectors.