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ES2501: Statics/Unit 8-1: Moment of Force (2D cases)

Motivation:. door. ES2501: Statics/Unit 8-1: Moment of Force (2D cases). Forces distributed over a rigid body may cause rotation. Effects of a force on rotation depend not only on magnitude and direction of the force but also on where it applies. Concept of moment.

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ES2501: Statics/Unit 8-1: Moment of Force (2D cases)

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  1. Motivation: door ES2501: Statics/Unit 8-1: Moment of Force (2D cases) Forces distributed over a rigid body may cause rotation. Effects of a force on rotation depend not only on magnitude and direction of the force but also on where it applies. Concept of moment To open the door where is better to apply the force? Definition of Moment of a Force about a point: Distance of the force to its line of action Magnitude of the force Sign convention: “+“---- counterclockwise “-” --- clockwise Moment of a force about point O Moment is additive: Line of action of the force Dimension: [M}=[F}{L] Unit: N-m; lb-ft

  2. General Comments: ES2501: Statics/Unit 8-2: Moment of Force (2D cases) Moment of a force about a point is zero if the point is on the line of action of the force. Sign convention: “+“---- counterclockwise “-” --- clockwise Line of action of the force d must be the perpendicular distance to the line of action of the force Alternative formula based on the additive property of moment Equivalence? correct d Line of action of the force A is ANY point on the Line of action of the force

  3. Example: Find the moment of the force shown about point O ES2501: Statics/Unit 8-3: Moment of Force (2D cases) (1) By basic definition Clockwise (2) By Cartesian compopnents (2) By the cross-product definition The same answer !

  4. Moment of a Couple ES2501: Statics/Unit 8-4: Moment of Force (2D cases) Couple ----- a pair of forces with the same magnitude and opposite direction Moments of a Couple: Distance between lines of action of the couple of force Magnitude of force Moment of the couple Sign convention Moment of a couple about ANY point is the same!!

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