The left diagram illustrates a balanced situation (equilibrium) where a ruler is
pivoted in the middle and two weights w1 and w2 are placed at distances d1 and
d2 from the pivot point.

Remember weight = force in newtons.

The weights hang vertically so the force due to gravity is
acting perpendicularly (at 90^{o}) to the ruler

For the ruler to be balanced in a perfect horizontal position
the two turning forces must be equal.

Here we use the terms **clockwise moment** and
**anticlockwise moment** for the two turning effects of the forces involved.

anticlockwise moment = w1 x d1 (left-hand side of pivot),
clockwise moment = w2 x d2 (right-hand side of pivot)

so when **
w1d1 = w2d2**

the** ruler is balanced horizontally**, at
equilibrium when the turning effects of the forces are equal.

This situation conforms with the **principle
of moments** which
states that when the total sum of the anti clockwise
moments is
equal to the total sum of the clockwise
moments **the system is in equilibrium**
and the object (system) will NOT turn**.**

When a system is stable (no movement) or balanced it is said to be in
equilibrium as all the forces acting on the system cancel each other out.

You
see this when you do a simple experiment balancing a rule on a pencil and
putting small weights on either side until balanced.

Similarly, when a the nut of a bolt is tightened, there comes a point when
the moment you are applying is balanced by the opposing moment of the bolt
and nut and you cannot tighten the nut anymore.

The
middle of a** seesaw** is the pivot point. If two people of equal weight
sit on either end, the seesaw is **balanced** horizontally - the
clockwise and anticlockwise moments are equal. If the two people differ in
weight, the seesaw will drop down on the side of the heaviest person because
the clockwise and anticlockwise moments are unequal.

The direction of rotation i.e. clockwise or anticlockwise, will be
decided on the relative weights (forces) at each end of the seesaw. One
end will fall in the direction of the largest moment

**
Make sure you have no problem
with unit conversions!**

**1 kg = 1000 g** and **100 cm = 1 m,**

and here for
simplicity, assume **g = 10 N/kg** (weight = mass x force of gravity)

The beam of the scales should be horizontal
when the bowl and weights plate are empty (d1 = d2, w1 = w2).

In other words d1w1 = d2w2

When the object to be weighed is placed in
the dish, the scales tip anticlockwise down on the left.

You then add weights until the beam is
horizontally balanced again, thus giving the weight of the material e.g. flour
in the bowl.

**
Examples of simple calculations using the above situations**

Predict what happens in the following situations Q1(a) to (c)

**
Q1(a)** Suppose d1 = 20 cm, w1 = mass of 25 g, d2 = 10 cm,
w2 = mass of 50 g

**but is it balanced?
Any clockwise or anticlockwise movement?**

Worked out ANSWERS

**
Q1(b)** Suppose d1 is 14 cm, w1 = mass of 52 g, d2 = 12
cm, w2 = mass of 60 g

**
**

**but is it balanced?
Any clockwise or anticlockwise movement?**

Worked out ANSWERS

**
Q1(c)** Suppose d1 is 2.5 m, w1 = mass of 55 kg, d2 = 3.0
m, w2 = mass of 50 kg

**but is it balanced?**

**but is it balanced?
Any clockwise or anticlockwise movement?**

Worked out ANSWERS