COUPLE

MOMENTS:

The moment (or torque) of a force about a turning point is the force multiplied by the perpendicular distance to the force from the turning point.

moments are measured in newton metres (Nm).

Moment = F d

• F = the force in newtons (N)
• d = perpendicular distance in metres (m)

Example; A 10N force acts at a perpendicular distance of 0.50m from the turning point. What is the moment of the force?

Moment = Fd
= 10 x 0.50
= 5.0 Nm

 

The principle of moments:

” When an object is in equilibrium the sum of the anticlockwise moments about a turning point must be equal to the sum of the clockwise moments.”

sum of anticlockwise moments= sum clockwise moments
sum of anticlockwise moments = sum clockwise moments
F₁ x d₁ = F₂ x d₂
sum of anticlockwise moments = sum clockwise moments
F₁ x d₁ =  (F₂ x d₂) +  (F₃ x d₃)

COUPLE:

Acouple is two equal forces which act in opposite directs on an object but not through the same point so they produce a turning effect.

The moment (or torque) of a couple is calculated by multiplying the size of one of the force (F) by the perpendicular distance between the two forces (s).

Moment of couple = Fs

The main characteristics of couple:

1. The algebraic sum of the forces, having the couple, is zero.

2. The algebraic sum of moment of the forces, constituting couple, about any point is the same, and equal to the moment of couple itself.

3. A couple can’t be balanced by a single force, but can be balanced only by a couple, however of opposite sense.

4. Any number of coplanar couples can be reduced to single couple, whose magnitude will be equal to algebraic sum of moments of all the couples.