Chapter4- Moment of a Force~Couple

# Chapter4- Moment of a Force~Couple - Moment of a Force...

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PCS211 – Physics II: Mechanics Moment of a Force Lectures 8-10 (Chapter 4) Dr. Marina Milner-Bolotin [email protected] Check Blackboard for course web site!

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PCS211 – Physics II: Mechanics Part I: Lecture 8 Goals for Lecture 8: Understand and define moment of a force Determine moments of a force in 2-D and 3-D. Practice problem solving involving these concepts! 2
PCS211 – Physics II: Mechanics Moment of a Force – Scalar Formulation (Section 4.1) 3 The moment of a force about a point provides a measure of the tendency for rotation (it is sometimes called torque).

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PCS211 – Physics II: Mechanics Torque – or Moment of a Force 4 TORQUE (in Latin torque means “to twist”): measures the tendency of a force F to rotate an object about some axis; Torque is a vector quantity; Torque or Moment should not be confused with Force or Work !!! Force and Moment are physical quantities with different dimensions. Though Work and Moment have the same dimensions, work is a scalar and Moment is a vector. Their units are different : [torque or moment] = N.m while [work] = Joule
PCS211 – Physics II: Mechanics Units for Moment of a Force (Torque) 5 Newtons.metres (SI units) abbreviated as N.m , foot.pounds (British system) abbreviated as ftlb , inch.pounds (British system) abbreviated as inlb . The conversion between inlb and ftlb is: 1 ftlb = 12 inlb The conversion between inlb and N.m is: 1 inlb = 0.113 N.m

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PCS211 – Physics II: Mechanics Moment of a Force – Scalar Formulation 6 In the 2-D case, the magnitude of the moment is M o = F d where d is the perpendicular distance from point O to the line of action of the force. In 2-D, the direction of M O is either clockwise or counter-clockwise depending on the tendency for rotation.
PCS211 – Physics II: Mechanics Moment of a Force – Scalar Formulation 7 Moment Arm , also called Lever Arm , is the name given to the perpendicular distance from the line of action of the force to the axis of rotation. The way the rotation goes is referred to as Sense Fd rF M = α sin line of action sense F lever arm Pivot d r α F R F T The components of the force F are: the tangential F T component that tends to cause rotation; the radial F R component that will never cause rotation;

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PCS211 – Physics II: Mechanics Moment of a Force – Scalar Formulation 8 Often it is easier to determine M O by using the components of F as shown. Using this approach, M O = (F Y a) – (F X b). Note the different signs on the terms! The typical sign convention for a moment in 2-D is that counter-clockwise is considered positive . We can determine the direction of rotation by imagining the body pinned at O and deciding which way the body would rotate because of the force. a b O F F x F y
PCS211 – Physics II: Mechanics Moment of a Force – General Definition 9 The magnitude of the moment of the force F (or torque) relative to point A is: where, r is the distance between the pivot point A, and the point of application of F; The directions of r and F make an angle α ; d is the perpendicular distance from the pivot point to the line of

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Chapter4- Moment of a Force~Couple - Moment of a Force...

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