1. Moment of a Force

2. Objectives
Introduce the concept of the moment of a force and show how to calculate it in 2 dimensions.
Define the moment of a couple.
Present methods for determining the resultants force systems.

3. Force F tends to rotate the beam clockwise about A with moment
MA = FdA
Force F tends to rotate the beam counterclockwise about B with moment
MB = FdB
Hence support at A prevents
the rotation

4. Magnitude For magnitude of MO, MO = Fd
where d = moment arm or perpendicular distance from the axis at point O to its line of action of the force
Units for moment is N.m

5. Direction
FMD

6. Example1
For each case, find the moment
of the force about the point O

7. A
MO =

8. B
MO =

9. C m N m m
MO =

10. D m m m N
MO =

11. E
MO =

12. Example2 Determine the moment of the 800 N
force about points A, B, C, and D

13. Resultant Moment

14. Principles of Moments Also known as Varignon’s Theorem
“Moment of a force about a point is equal to the sum of the moments of the force’s components about the point”

15. Example3
Determine the resultant moment of the four forces.

16. Example4
Determine the moment of the force about A.

18. Example5
Determine the moment of the force about 0.

20. Moment of a Couple A couple is two parallel forces having the same
magnitude and opposite directions separated by
a distance d.

21. Moment of a Couple Resultant Force is zero.
Effect of couple is a moment

22. Moment of a Couple A Couple consists of two parallel forces,
equal magnitude, opposite directions,
and separated a distant “d” apart.
A Couple Moment about any point O equals the sum of the moments of both forces.

23. Example6
150N
600N
100N
250N
A 4.80m long beam is subjected to the forces shown.
Reduce the given system of forces to
an equivalent force couple system at A
b) single force or resultant

24. Important Points
The moment of a force indicates the tendency of the body to cause rotation about a point.
Magnitude M=Fd d is  distance from point O to line of action of F
3. Principle of Moments

25. QUIZ 1. What is the moment of the 10 N force about point A (MA)?
A) 3 N·m B) 36 N·m C) 12 N·m
D) (12/3) N·m E) 7 N·m
• A
d = 3 m
F = 12 N

26. QUIZ
2. Using the CW direction as positive, the net moment of the two forces about point P is
A) 10 N ·m B) 20 N ·m C) N ·m
D) 40 N ·m E) N ·m
10 N
3 m P m
5 N

27. QUIZ
3. If F1 = 1 N, x1 = 1 m, F2 = 2 N and x2 = 2 m, what is the location of FR, i.e., the distance x.
A) 1 m B) 1.33 m C) 1.5 m
D) 1.67 m E) 2 m F R x 2 1