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Moments

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Moment The moment of a force is a measure of the tendency of the force to rotate the body upon which it acts.

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Terminology = F pivot distance = d lever arm The distance must be perpendicular to the force.

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Moments Formula = F pivot Moment M M = d x F distance = d

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Units for Moments ForceDistanceMoment English Customary Pound force (lbf) Foot (ft)lbf-ft SINewton (N)Meter (m)N-m

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Rotation Direction In order to add moments, it is important to know if the direction is clockwise (CW) or counterclockwise (CCW). CCW is positive CW is negative

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Right-Hand Rule Curl your fingers to match the direction of rotation. Thumb is pointing.... Up = Positive Down = Negative Toward You = Positive Away from You = Negative +

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Right-Hand Rule THUMB POINTS TOWARD YOU POSITIVE

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Right-Hand Rule THUMB POINTS AWAY FROM YOU NEGATIVE

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Moment Calculations Wrench F = 20. lb d = 9.0 in. M = d x F Use the right-hand rule to determine positive and negative. d = 9.0 in. =.75 ft M = -(20. lb x.75 ft) M = -15 lb-ft (15 lb-ft clockwise) ¯

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Moment Calculations Longer Wrench F = 20. lb d = 1.0 ft M = d x F M = -(20. lb x 1.0 ft) M = -20. lb-ft ¯

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Moment Calculations L - Shaped Wrench F = 20. lb d = 3 in. =.25 ft M = d x F M = -(20. lb x.25 ft) M = -5 lb-ft ¯ 3 in. d = 1.0 ft

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Moment Calculations Z - Shaped Wrench F = 20. lb d = 8 in. + 10 in. = 1.5 ft M = d x F M = -(20. lb x 1.5 ft) M = -30. lb-ft ¯ 8 in. 9 in. 10. in.

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d = r = 50. cm = 0.50 m M = d x F Use the right-hand rule to determine positive and negative. M = 100 N x 0.50 m M = 50 N-m Moment Calculations Wheel and Axle F = 100 N r = 50. cm +

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50. o F y = Fsin50.° = (100. N)(.766) F y = 76.6N d = r = 50. cm = 0.50 m M = d x F y M = 76.6 N x 0.50 m M = 38 N-m Moment Calculations Wheel and Axle F = 100. N r = 50. cm FyFy

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What is Equilibrium? The state of a body or physical system with an unchanging rotational motion. Two cases for that condition: 1.Object is not rotating OR 2.Object is spinning at a constant speed In either case rotation forces are balanced: The sum of all moments about any point or axis is zero. ΣM = 0 M 1 + M 2 + M 3... = 0

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Moment Calculations See-Saw

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ΣM = 0 M 1 + M 2 = 0 Use the right-hand rule to determine positive and negative. M 1 = -M 2 d 1 x F 1 = d 2 x F 2 25lb x 4.0ft - 40. lb x d 2 =0 100 lb-ft = 40. lb x d 2 Moment Calculations See-Saw F 1 = 25 lb F 2 = 40. lb d 1 = 4.0 ft d 2 = ? ft 40. lb 40. lb 2.5 ft = d 2 + ¯

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ΣM = 0 M B + M C = 0 M B = -M C d AB x R By = d AC x F C 10.00 ft x R By = 3.00 ft x 35.0 lb 10.0 ft x R By = 105 lb-ft Moment Calculations Loaded Beam d AB = 10.00 ft d AC = 3.00 ft A C B R Ay F C = 35.0 lb R By 10.00 ft 10.00 ft R By = 10.5 lb R Ay + R By = 35.0 lb R Ay = 35.0 lb – 10.5 lb = 24.5 lb Select A as the pivot location. Solve for R By

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A B C D F c = 600. lb Moment Calculations Truss 24 ft 8 ft 12 ft F B = 500. lb Replace the pinned and roller supports with reaction forces. R Ay R Ax R Dy d AC = 24 ft d CD = 8 ft d CB = 12 ft d AD = 32 ft

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A B C D F c = 600. lb Moment Calculations Truss d AC = 24 ft d CD = 8 ft d CB = 12 ft d AD = 32 ft 24 ft 8 ft 12 ft F B = 500. lb R Ay R Ax R Dy Select A as the axis of rotation. Solve for R DY 12 ft ΣM = 0 M D – M B – M C = 0 M D = M B + M C d AD x R Dy = (d CB x F B ) + (d AC x F C ) 32 ft x R Dy = (12 ft x 500. lb) + (24 ft x 600. lb) R Dy x 32 ft = 6000 lb-ft + 14400 lb-ft R Dy x 32 ft = 20400 lb-ft 32 ft 32 ft R DY = 640 lb

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