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Terminology

What Is a Moment?. distance. FORCE. Terminology. 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. = F. lever arm. pivot. = D. distance. FORCE. Formula for Moment. = F. pivot. = D. Moment. M. M = F x D.

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Terminology

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

  2. distance FORCE Formula for Moment = F pivot = D Moment M M = F x D

  3. Units for Moments The Right Hand Rule + counterclockwise

  4. FORCE Right Hand Rule THUMB POINTS TOWARD YOU POSITIVE

  5. FORCE Right Hand Rule THUMB POINTS AWAY FROM YOU NEGATIVE

  6. ¯ FORCE D = 9 in. 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) M = -15 lb-ft (15 lb-ft clockwise)

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

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

  9. ¯ FORCE Moment Calculations F = 20 lb • Offset Wrench 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. 8 in. 10 in.

  10. r = 50 cm + Moment Calculations • Wheel and Axle D = r = 50 cm = .5 m M = F x D ***Use the right hand rule to determine positive and negative. M = 100 N x .5 m M = 50 N-m F = 100 N

  11. r = 50 cm 50o 50o Fy Moment Calculations • Wheel and Axle Fy = Fsin50° = (100 N)(.766) Fy = 76.6 N D = r = 50 cm = .5 m M = Fy x D M = 76.6 N x .5 m M = 38.3 N-m Fx F = 100 N

  12. ¯ + D1 = 4 ft D2 = ? ft Moment Calculations ΣM = 0 M1 + (–M2) = 0 ***Use the right hand rule to determine positive and negative. M1 = M2 F1 x D1 = F2 x D2 25 lb x 4 ft = 40 lb x D2 100 lb-ft = 40 lb x D2 • See-Saw F2 = 40 lb F1 = 25 lb 40 lb 40 lb 2.5 ft = D2

  13. 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. Thesum of all moments about any point or axis is zero. ΣM = 0 M1 + M2 + M3 . . . = 0

  14. DAB = 10 ft DAC= 3 ft Moment Calculations Select the pivot location A. Solve for RB. • Loaded Beam ΣM = 0 MB + (–MC)= 0 MB = MC RB x DAB = FC x DAC RB x 10 ft = 35 lb x 3 ft RB x 10 ft = 105 lb-ft C 10 ft 10 ft A B RB = 10.5 lb RA + RB = 35 lb RA = 35 lb – 10.5 lb = 24.5 lb FC = 35 lb RA RB

  15. Moment Calculations Truss FB = 500 lb B Replace the pinned and rolling supports with reaction forces. 12 ft RAX A C 24 ft 8 ft D DAC = 24 ft DCD = 8 ft DCB = 12 ft DAD = 32 ft RAY Fc = 600 lb RDY

  16. Moment Calculations Select the pivot at A. Solve for RDY. Truss ΣM = 0 MD – MB – MC = 0 MD = MB + MC RDY x DAD = (FB x DCB) + (FC x DAC) RDY x 32 ft = (500 lb x 12 ft) + (600 lb x 24 ft) RDY x 32 ft = 6000 lb-ft + 14400 lb-ft RDY x 32 ft = 20400 lb-ft FB = 500 lb B 12 ft 12 ft RAX A C 8 ft 24 ft D 32 ft 32 ft DAC = 24 ft DCD = 8 ft DCB = 12 ft DAD = 32 ft RDY = 637.5 lb RAY Fc = 600 lb RDY

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

  18. Moments on an Airplane PATH WITH MOMENTS Translation and Rotation PATH WITHOUT MOMENTS Pure Translation

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