1. Moments Moments Principles of EngineeringTM
Unit 4 – Lesson Statics
Moments

2. Moments
Moment
Principles of EngineeringTM
Unit 4 – Lesson Statics
The moment of a force is a measure of the tendency of the force to rotate the body upon which it acts.
FORCE
The force applied to drive the bolt produces a measurable moment, and the wrench rotates about the axis of the bolt.

3. Terminology = F FORCE pivot = D distance lever arm
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Terminology
FORCE
= F
distance
lever arm
pivot
= D
The distance must be perpendicular to the force.

4. Moment M M = F x D Moments Formula = F FORCE pivot = D distance
Principles of EngineeringTM
Unit 4 – Lesson Statics
Moments Formula
FORCE
= F
distance
pivot
= D
Moment
M = F x D M

5. Units for Moments Force Distance Moment English Customary
Principles of EngineeringTM
Unit 4 – Lesson Statics
Force
Distance
Moment
English
Customary
Pound force (lbf)
Foot (ft)
lb-ft SI
Newton (N)
Meter (m)
N-m

6. Rotation Direction CCW is positive CW is negative
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
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

7. + Right-Hand Rule counterclockwise
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
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
counterclockwise

8. THUMB POINTS TOWARD YOU
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Right-Hand Rule
FORCE
THUMB POINTS TOWARD YOU
POSITIVE

9. THUMB POINTS AWAY FROM YOU
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Right-Hand Rule
THUMB POINTS AWAY FROM YOU
FORCE
NEGATIVE

10. ¯ Moment Calculations FORCE Wrench F = 20. lb D = 9.0 in. M = -(F x D)
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Moment Calculations
Wrench
F = 20. lb
FORCE
M = -(F x D)
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)
D = 9.0 in.

11. ¯ Moment Calculations FORCE Longer Wrench F = 20. lb D = 1.0 ft
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Moment Calculations
Longer Wrench
F = 20. lb
FORCE
M = -(F x D)
M = -(20. lb x 1.0 ft)
M = lb-ft
D = 1.0 ft

12. ¯ Moment Calculations FORCE L - Shaped Wrench F = 20. lb
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Moment Calculations
L - Shaped Wrench
FORCE
F = 20. lb
D = 3 in. = .25 ft
M = -(F x D)
M = -(20. lb x .25 ft)
M = -5 lb-ft
3 in.

13. ¯ Moment Calculations FORCE Z - Shaped Wrench F = 20. lb
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Moment Calculations
FORCE
Z - Shaped Wrench
F = 20. lb
D = 8 in in. = 1.5 ft
M = -(F x D)
M = -(20. lb x 1.5 ft)
M = lb-ft
9 in.
8 in.
10. in.

14. Moment Calculations + Wheel and Axle D = r = 50. cm = 0.50 m M = F x D
Moments
Moment Calculations
Principles of EngineeringTM
Unit 4 – Lesson Statics
Wheel and Axle
r = 50. cm
D = r = 50. cm = 0.50 m
M = F x D
Use the right-hand rule to determine positive and negative.
M = 100 N x 0.50 m
M = 50 N-m +
F = 100 N

15. Moment Calculations Wheel and Axle Fy = Fsin50.° = (100. N)(.7660)
Moments
Moment Calculations
Principles of EngineeringTM
Unit 4 – Lesson Statics
Wheel and Axle
r = 50. cm
Fy = Fsin50.° = (100. N)(.7660)
Fy = N
D = r = 50. cm = 0.50 m
M = Fy x D
M = N x 0.50 m
M = 38 N-m
50.o Fy
50.o
F = 100. N

16. What is Equilibrium? ΣM = 0 M1 + M2 + M3 . . . = 0
Moments
What is Equilibrium?
Principles of EngineeringTM
Unit 4 – Lesson Statics
The state of a body or physical system at rest or in unaccelerated motion in which the resultant of all forces acting on the body is zero. The sum of all moments about any point or axis is zero.
ΣM = 0
M1 + M2 + M = 0

17. Moment Calculations See-Saw Moments Principles of EngineeringTM
Unit 4 – Lesson Statics
Moment Calculations
See-Saw

18. ¯ Moment Calculations + See-Saw ΣM = 0 M1 + (–M2) = 0 M1 = M2
Moments
Moment Calculations
Principles of EngineeringTM
Unit 4 – Lesson Statics
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 4.0 ft = 40. lb x D2
100 lb-ft = 40. lb x D2
See-Saw
F2 = 40. lb
F1 = 25 lb
40. lb lb +
2.5 ft = D2
D1 = 4.0 ft
D2 = ? ft

19. Moment Calculations Loaded Beam C 10.00 ft 10.00 ft A B
Moments
Moment Calculations
Principles of EngineeringTM
Unit 4 – Lesson Statics
Loaded Beam
Select A as the pivot location. Solve for RB.
ΣM = 0
MB + (–MC) = 0
MB = MC
RB x DAB = FC x DAC
RB x ft = 35.0 lb x 3.00 ft
RB x ft = 105 lb-ft
DAB = ft
DAC= 3.00 ft C
10.00 ft ft A B
RB = 10.5 lb
RA + RB = 35.0 lb
RA = 35.0 lb – 10.5 lb = 24.5 lb
FC = 35.0 lb RA RB

20. Moment Calculations Truss FB = 500. lb B RAX A C D RAY Fc = 600. lb
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Moment Calculations
Truss
FB = 500. lb B
Replace the pinned and roller supports with reaction forces.
12 ft
RAX A
24 ft C
8 ft D
DAC = 24 ft
DCD = 8 ft
DCB = 12 ft
DAD = 32 ft
RAY
Fc = 600. lb
RDY

21. Moment Calculations Truss FB = 500. lb B RAX A C D RAY Fc = 600. lb
Moments
Principles of EngineeringTM
Unit 4 – Lesson Statics
Moment Calculations
Truss
Select A as the axis of rotation. Solve for RDY.
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 lb-ft
RDY x 32 ft = lb-ft
FB = 500. lb B
12 ft
12 ft
RAX A
24 ft C
8 ft D
32 ft ft
DAC = 24 ft
DCD = 8 ft
DCB = 12 ft
DAD = 32 ft
RDY = 640 lb
RAY
Fc = 600. lb
RDY