1) Moment of a force is a measure of the tendency of a force to cause rotation about a point or axis. 2) The magnitude of the moment of a force is equal to the product of the force and the perpendicular distance (moment arm) from the axis to the line of action of the force. 3) The direction of the moment vector is determined using the right hand rule, with the thumb pointing along the moment axis in the direction of rotation.

1. 4.1 Moment of a Force
– Scalar Formation
Moment of a force about a point or axis – a
measure of the tendency of the force to
cause a body to rotate about the point or axis
Case 1
Consider horizontal force Fx,
which acts perpendicular to
the handle of the wrench and
is located dy from the point O

2. 4.1 Moment of a Force
– Scalar Formation
Fx tends to turn the pipe about the z axis
The larger the force or the distance dy, the
greater the turning effect
Torque – tendency of
rotation caused by Fx
or simple moment (Mo) z

3. 4.1 Moment of a Force
– Scalar Formation
Moment axis (z) is perpendicular to shaded
plane (x-y)
Fx and dy lies on the shaded plane (x-y)
Moment axis (z) intersects
the plane at point O

4. 4.1 Moment of a Force
– Scalar Formation
Case 2
Apply force Fz to the wrench
Pipe does not rotate about z axis
Tendency to rotate about x axis
The pipe may not actually
rotate Fz creates tendency
for rotation so moment
(Mo) x is produced

5. 4.1 Moment of a Force
– Scalar Formation
Case 2
Moment axis (x) is perpendicular to shaded
plane (y-z)
Fz and dy lies on the shaded plane (y-z)

6. 4.1 Moment of a Force
– Scalar Formation
Case 3
Apply force Fy to the wrench
No moment is produced about point O
Lack of tendency to rotate
as line of action passes
through O

7. 4.1 Moment of a Force
– Scalar Formation
In General
Consider the force F and the point O which lies in
the shaded plane
The moment MO about point O,
or about an axis passing
through O and perpendicular
to the plane, is a vector quantity
Moment MO has its specified
magnitude and direction

8. 4.1 Moment of a Force
– Scalar Formation
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

9. 4.1 Moment of a Force
– Scalar Formation
Direction
Direction of MO is specified by
using “right hand rule”
- fingers of the right hand are
curled to follow the sense of
rotation when force rotates about
point O

10. 4.1 Moment of a Force
– Scalar Formation
Direction
- Thumb points along the
moment axis to give the
direction and sense of the
moment vector
- Moment vector is upwards and
perpendicular to the shaded
plane

11. 4.1 Moment of a Force
– Scalar Formation
Direction
MO is shown by a vector arrow
with a curl to distinguish it from
force vector
Example (Fig b)
MO is represented by the
counterclockwise curl, which
indicates the action of F

12. 4.1 Moment of a Force
– Scalar Formation
Direction
Arrowhead shows the sense of
rotation caused by F
Using the right hand rule, the
direction and sense of the moment
vector points out of the page
In 2D problems, moment of the
force is found about a point O

13. 4.1 Moment of a Force
– Scalar Formation
Direction
Moment acts about an axis
perpendicular to the plane
containing F and d
Moment axis intersects
the plane at point O

14. 4.1 Moment of a Force
– Scalar Formation
Resultant Moment of a System of
Coplanar Forces
Resultant moment, MRo = addition of the
moments of all the forces algebraically since
all moment forces are collinear
MRo = ∑Fd
taking clockwise to be positive

15. 4.1 Moment of a Force
– Scalar Formation
Resultant Moment of a System of
Coplanar Forces
A clockwise curl is written along the equation
to indicate that a positive moment if directed
along the
+ z axis and negative
along the – z axis

16. 4.1 Moment of a Force
– Scalar Formation
Moment of a force does not always cause rotation
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

17. 4.1 Moment of a Force
– Scalar Formation
Example 4.1
For each case, determine the moment of the
force about point O

18. 4.1 Moment of a Force
– Scalar Formation
Solution
Line of action is extended as a dashed line to
establish moment arm d
Tendency to rotate is indicated and the orbit is
shown as a colored curl
(a ) M o = (100 N )(2m) = 200 N .m(CW )
(b) M o = (50 N )(0.75m) = 37.5 N .m(CW )

19. 4.1 Moment of a Force
– Scalar Formation
Solution
(c) M o = (40 N )(4m + 2 cos 30o m) = 229 N .m(CW )
(d ) M o = (60 N )(1sin 45o m) = 42.4 N .m(CCW )
(e) M o = (7kN )(4m − 1m) = 21.0kN .m(CCW )

20. 4.1 Moment of a Force
– Scalar Formation
Example 4.2
Determine the moments of
the 800N force acting on the
frame about points A, B, C
and D.

21. 4.1 Moment of a Force –
Scalar Formation
Solution
Scalar Analysis
M A = (800 N )(2.5m) = 2000 N .m(CW )
M B = (800 N )(1.5m) = 1200 N .m(CW )
M C = (800 N )(0m) = 0kN .m
Line of action of F passes through C
M D = (800 N )(0.5m) = 400 N .m(CCW )

22. 4.1 Moment of a Force
– Scalar Formation
Example 4.3
Determine the resultant moment of the four
forces acting on the rod about point O

23. 4.1 Moment of a Force –
Scalar Formation
Solution
Assume positive moments acts in the +k
direction, CCW
M Ro = ∑ Fd
M Ro = (−50 N )(2m) + (60 N )(0m) + (20 N )(3 sin 30o m)
− (40 N )(4m + 3 cos 30o m)
= −334 N .m
= 334 N .m(CW )