Page 68 - Mechanical Engineer's Data Handbook

APPLIED MECHANICS 57

Couple

If two equal and opposite forces have parallel lines of
action a distance a apart, the moment about any point
0 at distance d from one of the lines of action is
M = F, - F(d -a)= Fa
This is independant of d and the resultant force is zero.
Such a moment is called a ‘couple’.
Balance of forces

A system of forces is balanced, i.e. in equilibrium, when
the resultant F, is zero, in which case its components
F, and F, are each zero.

2.1.3 Moment of a force, couple F

The moment of a force F about a point 0 at a
perpendicular distanced from its line of action, is equal
to Fd.

Resolution of a moment into a force and a
couple
Resultant of several moments For a force F at a from point 0; equal and opposite
if
forces are applied at 0, then the result is a couple Fa
If forces F,, F,, etc., act on a body at perpendicular and a net force F.
distances d,, d,, etc., from a point 0, the moments are,
M,=F,d,, M2=Fzdz, etc. about 0
The resultant moment is M,= M, i- M,+ . . .
Clockwise moments are reckoned positive and
counterclockwise moments negative. If the moments
‘balance’ M,=O and the system is in equilibrium.

General condition for equilibrium of a body

Complete equilibrium exists when both the forces and
the moments balance, Le. F,=O and M,=O.

2. I .4 Linear and circular motion

Relationships for distance travelled, velocity and time
of travel are given for a constant linear acceleration.