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Unformatted text preview: MOMENTS Moment of a force in two dimensions In two dimensions, the moment of a force F about a point A is the product M = | F | d , (1) where | F | is the magnitude of F and d is the perpendicular distance from A to the line of action of F , as shown in Figure 1. We adopt the convention that counterclockwise moments are positive. . A F d Figure 1 The easiest way to find M is first to resolve F into its components F x , F y . The moment M is then the algebraic sum of the moments due to F x , F y and these are easily calculated because the corresponding perpendicular distances are now aligned with the coordinate axes. Example Find the moment (counterclockwise positive) of the 3 kN force in Figure 2(a) about the point A . The coordinates of the points A and B are in meters. Our first step is to resolve the force into its components F x = 3 cos(30) = 3 √ 3 2 ; F y = 3 sin(30) = 3 2 (2) as shown in Figure 2(b). 1 . . (4,8) (13,3) A B x y O 3 kN 30 o . . (4,8) (13,3) A B x y O o 9 5 3 cos (30 ) 3 sin (30 ) o (a) (b) Figure 2 The perpendicular distance from A to the line of action of F x is 5 m, as shown in the Figure, so the magnitude of the corresponding moment is 3 √ 3 2 × 5 . This moment is clockwise and hence negative according to the sign conven- tion. If you are uncertain whether it is clockwise or counter clockwise, pin the point A to the table with your finger and then push the paper at B in the direction of the 3 cos(30) force.the direction of the 3 cos(30) force....
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This note was uploaded on 10/05/2011 for the course MECHENG 211 taught by Professor ? during the Fall '07 term at University of Michigan.
- Fall '07