Moments Moment The moment of a force is a measure of the tendency of the force to rotate the body upon which it acts. FORCE Terminology pivot FORCE lever arm =F distance
=d The distance must be perpendicular to the force. Moments Formula FORCE pivot distance =d Moment M=dxF =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 count ercloc Toward You = Positive Away from You = Negative kwise FORCE Right-Hand Rule
POSITIVE B M U TH TS N POI ARD TOW U YO Right-Hand Rule FORCE NEGATIVE TH U M POIN B
TS AWA Y FR YOU OM Moment Calculations Wrench F = 20. lb FORCE M=dxF 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 FORCE d = 1.0 ft M=dxF M = -(20. lb x 1.0 ft) M = -20. lb-ft
Moment Calculations L - Shaped Wrench F = 20. lb 3 in. FORCE d = 3 in. = .25 ft M=dxF M = -(20. lb x .25 ft) M = -5 lb-ft d = 1.0 ft Moment Calculations F = 20. lb
FORCE Z - Shaped Wrench 9 in. d = 8 in. + 10 in. = 1.5 ft M=dxF 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=dxF 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 = Fsin50. = (100. N)(.766) Fy = 76.6N 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. M = 0M = 0 M1 + M 2 + M 3 . . . = 0 Moment Calculations See-Saw Moment Calculations M = 0M = 0 See-Saw
M1 + M2 = 0 Use the right-hand rule to determine positive and negative. M1 = -M2 F2 = 40. lb F1 = 25 lb d1 x F1 = d2 x F2 25lb x 4.0ft - 40. lb x d2=0 100 lb-ft = 40. lb x d2 40. lb + d1 = 4.0 ft 2.5 ft = d2
d2 = ? ft 40. lb Moment Calculations Loaded Beam Select A as the pivot location. Solve for RBy M = 0M = 0 MB + MC = 0 MB = -MC dAB = 10.00 ft dAC= 3.00 ft dAB x RBy = dAC 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 dAC = 24 ft dCD = 8 ft RAy dCB = 12 ft dAD = 32 ft Fc = 600. lb RDy
Moment Calculations Truss Select A as the axis of rotation. Solve for RDY M = 0M = 0 B FB = 500. lb MD MB MC = 0 MD = MB + MC 12 ft 12 ft
dAD x RDy = (dCB x FB) + (dAC 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
dAC = 24 ft RDY = 640 lb dCD = 8 ft RAy dCB = 12 ft dAD = 32 ft Fc = 600. lb RDy 32 ft
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