Moments
In a nutshell
A force applied to an object can cause a turning effect, this turning effect is called a moment. The point around which the rotation happens is called the pivot.
Equations
WORD EQUATION  SYMBOL EQUATION 
$moment = force \times distance$  $M = F \times d$ 
Variable definitions
QUANTITY NAME  SYMBOL  UNIT NAME  UNIT 
$moment$  $M$
 $newtonmetre$
 $Nm$ 
$force$
 $F$
 $newton$
 $N$

$distance$
 $d$
 $metre$  $m$

Moment calculations
A moment is the turning effect of a force, it depends on both the size of the force being applied and the distance which is normal to the direction of force. In other words, this is the perpendicular distance between the line of action of the force and the pivot. The line of action is the line along which the force acts, so the perpendicular distance is at right angles to the line of action of the force.
The size of a moment can be calculated using the following formula.
$moment = force \times distance$
$M = F \times d$
As force is measured in newtons and distance in metres; moments are measured in newtonmetres, $Nm$.
Example
If a child is sat at one end of a seesaw, what is the moment generated by their weight if they are sat $2 \space m$ away from the pivot and they weigh $300 \space N$?
First write out the quantities needed and make sure they are in the correct for,:
$f=300\,N\newline d=2\,m \space$
Next, write down the equation you need to use:
$moment = force \times distance$
Then, substitute the values into the equation:
$Moment = 300 \times 2 = 600$
Don't forget to include your units:
$600\,Nm$
A $300\,N$ child sat on a seesaw $2\,m$ away from the pivot has a moment of $\underline{600\,Nm}$.
Principle of moments
Sometimes objects can become balanced about their pivot, this happens when the clockwise moments equal the anticlockwise moments. The clockwise moments will cause a clockwise turning effect, and the anticlockwise moments will cause a turning effect in the opposite direction. This means that the object balances out in both directions and experiences no overall turning effect.
For an object in balance, the principle of moments holds:
$total \space anticlockwise \space moments = total \space clockwise \space moments$