Moments Moment The moment of a force is

Moments

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

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

Moments Formula =F pivot distance =d Moment M=dx. F

Units for Moments Force Distance Moment English Customary Pound force (lbf) Foot (ft) lbf-ft SI Newton (N) Meter (m) N-m

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

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 +

Right-Hand Rule POSITIVE B M U TH TS N POI ARD TOW U YO

Right-Hand Rule NEGATIVE THU M POIN B TS AWA Y FR YOU OM

Moment Calculations Wrench F = 20. lb M=dx. F ¯ Use the right-hand rule to determine positive and negative. d = 9. 0 in. =. 75 ft M = -(20. lb x. 75 ft) d = 9. 0 in. M = -15 lb-ft (15 lb-ft clockwise)

Moment Calculations Longer Wrench F = 20. lb M=dx. F ¯ M = -(20. lb x 1. 0 ft) M = -20. lb-ft d = 1. 0 ft

Moment Calculations L - Shaped Wrench F = 20. lb d = 3 in. =. 25 ft 3 in. M=dx. F M = -(20. lb x. 25 ft) ¯ M = -5 lb-ft d = 1. 0 ft

Moment Calculations Z - Shaped Wrench F = 20. lb 9 in. d = 8 in. + 10 in. = 1. 5 ft M=dx. F M = -(20. lb x 1. 5 ft) ¯ M = -30. lb-ft 8 in. 10. in.

Moment Calculations Wheel and Axle d = r = 50. cm = 0. 50 m r = 50. cm M=dx. F Use the right-hand rule to determine positive and negative. + F = 100 N M = 100 N x 0. 50 m M = 50 N-m

Moment Calculations Wheel and Axle r = 50. cm Fy = Fsin 50. ° = (100. N)(. 766) Fy = 76. 6 N d = r = 50. cm = 0. 50 m M = d x Fy M = 76. 6 N x 0. 50 m M = 38 N-m 50. o 50. o F = 100. N Fy

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

Moment Calculations See-Saw

Moment Calculations ΣM = 0 See-Saw M 1 + M 2 = 0 Use the right-hand rule to determine positive and negative. M 1 = -M 2 F 2 = 40. lb F 1 = 25 lb d 1 x F 1 = d 2 x F 2 25 lb x 4. 0 ft - 40. lb x d 2=0 100 lb-ft = 40. lb x d 2 40. lb ¯+ d 1 = 4. 0 ft 2. 5 ft = d 2 = ? ft 40. lb

Moment Calculations Loaded Beam Select A as the pivot location. Solve for RBy ΣM = 0 MB + MC = 0 MB = -MC d. AB = 10. 00 ft d. AC= 3. 00 ft d. AB x RBy = d. AC x FC 10. 00 ft x RBy = 3. 00 ft x 35. 0 lb C A B 105 lb-ft 10. 00 ft RBy = 10. 5 lb RAy + RBy = 35. 0 lb FC = 35. 0 lb RAy 10. 0 ft x RBy = 10. 00 ft RBy RAy = 35. 0 lb – 10. 5 lb = 24. 5 lb

Moment Calculations Truss FB = 500. lb Replace the pinned and roller supports with reaction forces. 12 ft B RAx A 24 ft C 8 ft D d. AC = 24 ft d. CD = 8 ft RAy d. CB = 12 ft d. AD = 32 ft Fc = 600. lb RDy

Moment Calculations Truss Select A as the axis of rotation. Solve for RDY ΣM = 0 B FB = 500. lb MD – M B – M C = 0 MD = M B + M C 12 ft d. AD x RDy = (d. CB x FB) + (d. AC x FC) RAx A 24 ft C 32 ft x RDy = (12 ft x 500. lb) + (24 ft x 600. lb) 8 ft RDy x 32 ft = 6000 lb-ft + 14400 lb-ft D RDy x 32 ft = 20400 lb-ft 32 ft d. AC = 24 ft RDY = 640 lb d. CD = 8 ft RAy d. CB = 12 ft d. AD = 32 ft Fc = 600. lb RDy 32 ft