Statics - Moments — The moment of a force about a point in a 2-D coordinate system

About this lesson

This unit introduces the concept of the moment of a force about a point in a 2D coordinate system. It defines the moment as the rotational effect of a force, calculated using the vector cross product M = r × F, where r is the position vector from the moment center to a point on the line of action of the force. The unit explains the moment arm, the algebraic measure (positive for counterclockwise, negative for clockwise), the norm of the moment, and that the moment is zero if the point lies on the line of action. It also covers Varignon's theorem (the moment of a force equals the sum of the moments of its components) and the general theorem of moments (the algebraic sum of moments of a system of forces equals the moment of the resultant). Worked examples and exercises involve finding moments about given points, determining perpendicular distances, and using moments to prove properties about the line of action of the resultant, such as parallelism or bisecting a segment. The unit also includes an introduction to coplanar forces, listing objectives for studying parallel forces and equilibrium, but the detailed content for those topics is not in this text.