The roles of science in national development

MOMENT OF A COUPLE
Today’s Objectives:
Students will be able to
a) define a couple, and,
b) determine the moment of a couple.

APPLICATIONS

A torque or moment of 12 N · m is required to rotate the wheel.
Which one of the two grips of the wheel above will require less force to rotate the wheel?

APPLICATIONS
(continued)

The crossbar lug wrench is being used to loosen a lug net. What is the effect of changing dimensions a, b, or c on the force that must be applied?

MOMENT OF A COUPLE
A couple is defined as two parallel forces with the same magnitude but opposite in direction separated by a perpendicular distance d.
The moment of a couple is defined as
MO = F d (using a scalar analysis) or as
MO = r × F (using a vector analysis).
Here r is any position vector from the line of action of –F to the line of action of F.

Couple moment only depends on F and d
F
d

A rOA rOB

-F

O

B

MB = + dF

What about point O, is MO = + dF too?

First note
=
=
=

MA = + dF

MOMENT OF A COUPLE
(continued)
The net external effect of a couple is that the net force equals zero and the magnitude of the net moment equals F d
Since the moment of a couple depends only on the distance between the forces, the moment of a couple is a free vector. It can be moved anywhere on the body and have the same external effect on the body.
Moments due to couples can be added using the same rules as adding any vectors.

EXAMPLE - SCALAR APPROACH
Given: Two couples act on the beam and d equals 8 ft.
Find: The resultant couple

Plan:
1) Resolve the forces in x and y directions so they can be treated as couples.
2) Determine the net moment due to the two couples.

EXAMPLE - SCALAR APPROACH
The x and y components of the top 60 lb force are:
(4/5)(60 lb) = 48 lb vertically up
(3/5)(60 lb) = 36 lb to the left
Similarly for the top 40 lb force:
(40 lb) (sin 30 ) up
The net moment equals to

(40 lb) (cos 30 ) to the