What have you learnt? moment of a force = F x d

The Principle of Moments states that when a body is in equilibrium, the sum of clockwise moments about a pivot is equal to the sum of anticlockwise moments about the same pivot.

A quick recap…A uniform metre rule balances horizontally about a pivot at its midpoint. A mass of weight 0.750 N is suspended at the 20.0 cm mark and another object of unknown mass is suspended at the 65.0 cm mark where the metre rule is horizontal. Determine the mass of the object.

Ruler demo The weight of the ruler caused a moment

about the pivot and hence it falls off.

So far, we have always take the point of the weight to be from the centre of the ruler.

But it may not be at the centre always!

Try finding the CG of the broom and pen!

Test Yourself

Test Yourself

Centre of Gravity (CG) The centre of gravity of any object is defined

as the point through which its whole weight appears to act.

How to find CG of irregular object?

Finding CG of irregular-shaped lamina

1. Make 3 small holes near the edge of the lamina.

2. Suspend the lamina through each hole using a pin.

3. Hang a plumbline on the pin in front of the lamina.

4. Slightly displace the lamina and release it.

5. When it comes to a stop, make 3 dots on the lamina along the plumbline.

6. Repeat for the other 2 holes.7. The point of intersection of the 3

lines is the position of the centre of gravity.

Example 1A uniform plank of weight 80 N rests centrally on a pair of trestles placed 2.0 m apart as shown in the diagram. A pile of bricks weighing 60 N is placed on the plank so that its weight acts at a point of 0.5 m from trestle B. (a) Find the upward forces exerted on the plank by each trestle.(b) The bricks are moved towards trestle B. What is the distance

from the centre of the plank such that the plank just lifts from trestle A?

A B

Stability The stability of an object is a measure of its

ability to return to its original position after it is slightly displaced.

Stable Equilibrium If the cone is slightly tilted,

Its centre of gravity rises before returning to its original height.

The line of action through its weight still lies within its base.

The moment of its weight about the contact point C causes the cone to return to its original position.

C

Unstable equilibrium If the cone is slightly tilted,

Its centre of gravity drops. The line of action through its weight lies outside its

base. The moment of its weight about the contact point

C causes the cone to topple.

C

Neutral equilibrium If the cone is slightly displaced,

Its centre of gravity remains at the same height. The moment of its weight about the point C is

zero. It stays in the position to which it is displaced.

C

Stable, Neutral or Unstable?

Factors affecting stability

Factors affecting stability

How much can they tilt?

Factors affecting stability Position of centre of gravity Base area

To increase stability of an object Centre of gravity should be as low as possible Base area should be as wide as possible

Balancing toys Where is the centre of gravity of these

objects?

Watch this: Balancing 2 forks on a toothpick http://www.youtube.com/watch?v=czsoNaf4MeY