Statics #04 | Moment of a Force: Turning Effect, Moment Arm and Varignon's Principle

Instructor: Dr. Süleyman Burak ÇELİK

A rusty bolt and a 250 mm wrench. Put your hand right next to the bolt and push with 80 N: nothing moves. Put the same 80 N at the end of the handle: the bolt turns. Same force, completely different result, because the turning effect depends on the force AND on how far from the pivot you apply it. That effect is the moment of a force. In this lesson we define the moment, learn its sign, compute it two different ways and work two full problems without skipping a single step. In this lesson: - Statics is two questions: are the forces in balance (ΣF = 0) and are the turning effects in balance (ΣM = 0); the moment is the building block of the second one - Definition: M = F · d, where d is the PERPENDICULAR distance from O to the line of action (not to the point of application) - Unit newton meter; sign: counterclockwise positive, clockwise negative - A force whose line of action passes through O has zero moment; why a long wrench works - Two routes: perpendicular arm (d = r sinθ) and components (F sinθ · r), Varignon's principle - Problem A: 0.25 m wrench, 80 N at 60 degrees to the handle → d = 0.2165 m → M = 17.32 N·m; the second route gives the same number; the 40 N component is wasted - Problem B: 3 m hinged beam, 400 N down at 1 m and 200 N at 30 degrees to the beam at 3 m → ΣM = minus 400 plus 300 = minus 100 N·m, clockwise; 266.7 N would balance it - Four classic traps: the wrong distance, forgetting the sign, mixing mm and N·m, thinking a big force means a big moment Chapters: 0:00 Intro 0:03 Two questions, one rusty bolt 1:05 What a moment is: definition, unit, sign 2:40 Two routes, same number: perpendicular arm and Varignon 4:22 Problem A: the wrench 6:47 Problem B: the hinged beam 10:02 Four traps and one habit 11:24 Summary and next lesson Next lesson: equilibrium of a rigid body, ΣF = 0 and ΣM = 0 together; beams, supports, real structures. Lesson 4 of the Statics (Engineering Mechanics) series for civil, mechanical and mechatronics engineering students.