Moments, Couples, Equipollence - TAM 210/211 Engineering...

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1 Lecture 6 Moments, Couples, Equipollence Stephen D. Downing Mechanical Science and Engineering © 2001 - 2007 University of Illinois Board of Trustees, All Rights Reserved TAM 210/211 Engineering Mechanics: Statics TAM 210/211 - Lecture 6 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 1 of 17 Moments of a Force About A Point ± The moment of a force about a fixed point is the measure of the tendency of the force to rotate the body about a fixed point. ± The moment of the force F about the point P is defined as ± Where is a vector from the point p to the line of the force ± The magnitude of the moment is equal to the magnitude of the force times the perpendicular distance to the line of action of the force. F r M P × = r F F 1 r 2 r p d 1 θ F Line of action of F d sin F r M P = θ = P M
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2 TAM 210/211 - Lecture 6 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 2 of 17 Moment of a Force About a Line ± The moment of a force F about a line L is the projection of the moment of the force about a point on the line L. ± It determines how much of the moment is projected on the line L, e.i. how much of the moment lines along L. F r p P M L M u ˆ Unit vector along the line u ˆ M u ˆ ) u ˆ M ( M L P L = = TAM 210/211 - Lecture 6 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 3 of 17 P P 1 P 2 Moments A C B F PA r P M L M
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3 TAM 210/211 - Lecture 6 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 4 of 17 Example ± What total moment does the force acting on the position (2,0,-4) m produce about the x-axis? ± Choose a point on the x-axis such as O=(0,0,0). Moment of about O is ± There is no part of M o in the x direction. N k ˆ 40 i ˆ 50 F = N k ˆ 40 i ˆ 50 F = j ˆ 120 40 0 50 4 0 2 k ˆ j ˆ i ˆ M O = = 0 i ˆ ) i ˆ M ( M O xaxis = = READ EXAMPLE 3.4 page 62-63 TAM 210/211 - Lecture 6 © 2008 Stephen Downing, University of Illinois at Urbana-Champaign, All Rights Reserved 5 of 17 Problem 3.26 ± Find the moment of the 2000N force shown about the diagonal line AB.
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This note was uploaded on 04/08/2008 for the course TAM 210/211 taught by Professor Downing during the Spring '08 term at University of Illinois at Urbana–Champaign.

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Moments, Couples, Equipollence - TAM 210/211 Engineering...

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