What Is a Moment The moment or torque

What Is a Moment? The moment or torque of a force is a measure of the tendency of the force to rotate the body upon which it acts about an axis. Terminology =F lever arm pivot distance =D

Formula for Moment =F pivot distance =D Moment M=Fx. D

Units for Moments Force English Pound (lb) Customary SI Newton (N) The Right Hand Rule + Distance Moment Foot (ft) lb-ft Meter (m) N-m

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 = -(F x D) ¯ ***Use the right hand rule to determine positive and negative. D = 9 in. =. 75 ft M = -(20 lb x. 75 ft) D = 9 in. M = -15 lb-ft (15 lb-ft clockwise)

Moment Calculations Longer Wrench F = 20 lb M = -(F x D) ¯ M = -(20 lb x 1 ft) M = -20 lb-ft D = 1 ft

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

Moment Calculations F = 20 lb Offset Wrench 8 in. D = 8 in. + 10 in. = 1. 5 ft M = -(F x D) M = -(20 lb x 1. 5 ft) ¯ M = -30 lb-ft 8 in. 10 in.

Moment Calculations Wheel and Axle D = r = 50 cm =. 5 m r = 50 cm M=Fx. D ***Use the right hand rule to determine positive and negative. + F = 100 N M = 100 N x. 5 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 =. 5 m M = Fy x D Fx M = 76. 6 N x. 5 m 50 o M = 38. 3 N-m 50 F = 100 N o Fy

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

What Is Equilibrium? The state of a body or physical system at rest or in unaccelerated motion in which the resultant of all forces acting on it is zero. The sum of all moments about any point or axis is zero. ΣM = 0 M 1 + M 2 + M 3. . . = 0

Moment Calculations Loaded Beam Select the pivot location A. Solve for RB. ΣM = 0 MB + (–MC) = 0 MB = M C DAB = 10 ft DAC= 3 ft RB x DAB = FC x DAC RB x 10 ft = 35 lb x 3 ft C A B RB = 10. 5 lb RA + RB = 35 lb FC = 35 lb RA RB x 10 ft = 105 lb-ft 10 ft RB RA = 35 lb – 10. 5 lb = 24. 5 lb

Moment Calculations Truss FB = 500 lb Replace the pinned and rolling 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 the pivot at A. Solve for RDY. ΣM = 0 B FB = 500 lb MD – M B – M C = 0 MD = M B + M C 12 ft RDY x DAD = (FB x DCB) + (FC x DAC) RAX A 24 ft C RDY x 32 ft = (500 lb x 12 ft) + (600 lb x 24 ft) 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 = 637. 5 lb DCD = 8 ft RAY DCB = 12 ft DAD = 32 ft Fc = 600 lb RDY 32 ft

Moments on An Airplane RUDDER Yaw AILERON Roll ELEVATORS Pitch AILERON Roll

Moments on an Airplane PA Tra TH WI T nsl atio H MO ME na nd N Rot TS atio n MOMENTS T U O H IT PATH W lation Pure Trans