Chapter 5: Turning Effects of Forces

Brief Recap [Centre of Gravity]

1. The centre of gravity of an object is defined as the point through which its whole weight appears to act for any orientation of the object.

2. Identify the positions of the centre of gravity of regular as well as irregular objects

Centre of Gravity

The centre of gravity of an object is defined as the point through which its whole weight appears to act for any orientation of the object

Regular and uniform objects

The geometrical centre of some common shapes-

This is also where the centre of gravity and the object’s weight, W, can be considered to act

For a triangle

The centre of gravity (and geometrical centre) is found by drawing a line from the corner to the opposite line’s midpoint

External CoG

For some objects the CoG is not located on the actual object -

Ring

Stool

2 uniform perpendicular planks

CoG of an irregular shape

Find the CoG of an irregular shaped lamina

a

bc

a bc

b

a

c

plumb line

hole

Pin held by clamp

Balancing Act!

Now, try to balance the object at that point…

Question- explain in terms of moments why the object can be balanced at this point?

a b

c

Answer- on one side of the point of CoG, the object’s weight is causing a turning effect. This is counter balanced on the other side where the weight is causing a turning effect in the opposite direction.

Let’s Watch A Short Clip…

A Simple Experiment

Stability

Stability refers to the ability of an object to return to its original position after it has been tilted slightly.

Case A: Base of cone in contact with ground

When the cone is tilted slightly,

1) Its centre of gravity rises and then falls back again

2) the line of action of its weight W lies insides the base area of the cone

3) the anticlockwise moment of its weight W about the point of contact C causes the cone to return to its original position

Hence, the cone is in stable equilibrium because when it is tilted slightly, it returns to its original position without toppling.

Anticlockwise

moment

Case B: Tip of cone in contact with ground

When the cone is tilted slightly,

1) its centre of gravity falls and continues to fall further

2) the line of action of its weight W lies outside the base area of the cone

3) the clockwise moment of its weight W about the point of contact C causes toppling

Hence, the cone is in unstable equilibrium because when it is tilted slightly, it topples over.

Clockwise

moment

Case C: Slant surface of cone in contact with ground

When the cone is tilted slightly,

1) its centre of gravity neither rises nor falls; it remains at the same level above the surface supporting it

2) the lines of action of the two forces W and R always coincide

3) there is no moment provided by its weight W about the point of contact C to turn the cone

Hence, the cone is in neutral equilibrium because when it is slightly displaced or rolled, it will stay in its new position.

No moment

Stability

For an object to start rotating it needs to have an unbalanced moment acting on it-

WW W

Stable

Pivot Pivot

Rotates Clockwise Rotates Anti-Clockwise

Stable Unstable

• An object becomes unstable when its Centre of

Gravity falls outside of the object’s base.

Why?

All of the object’s weight can be considered as acting

through the CoG. If this acts outside the base then it

will cause a turning effect or a moment

Factors affecting stability of objects

1. The base area of an object

(As wide as possible)

2. The height of the centre of gravity above the base of an object

(As low as possible)

To increase the stability of an object:

1. Broaden/widen the base area of the object

2. Add weights to the base of the object such that the CG becomes lower

The Traffic Cone

A great example of a VERY stable object.

What features of the cone make it so stable?

-Low Centre of Gravity

-Wide base

Balance and Sport

Balance and Sport

The Double Decker Bus

Each of the diagrams on the right represent a Double Decker bus with passengers inside.

Draw out and label the one which shows all passengers on

- the lower level

- the upper level

- both levels

Delete a word to complete the sentences

If more people sit upstairs on the bus the CoG will rise/fall. This will make the bus more stable/unstable and itcan be tilted by a greater/lesser angle

The bus will fall over when the CoG acts inside/outside of the bus’ base

A stable object has a low/high CoG and a narrow/wide base

Formula One Racing Car

The more stable a car, the faster it can go round sharp turns without overturning. Hence, all racing cars have a very wide base and a low centre of gravity)

Tightrope Walker

The tightrope walker has to position his centre of gravity directly above the metal wire in order to maintain his balance and not fall. If his centre of gravity is not aligned vertically with the wire, it will give rise to a moment that will rotate him about the wire. If the tightrope walker does not quickly realign his centre of gravity, he will fall.

The long balancing rope helps to lower his CG. By using a long drooping pole with weighted ends, his CG may actually lie below the wire. In this case, the tightrope walker will be more stable and will find it easier to balance on the rope.)

We have learnt…

1) State that stability refers to the ability of an object to return to its original

position after it has been tilted slightly

2) Describe qualitatively the effect of the position of the centre of gravity on

the stability of objects

3) Identify and describe three different cases of equilibrium namely stable

equilibrium, unstable equilibrium and neutral equilibrium in terms of

centre of gravity and moments of its weight about the point of contact

4) Identify that in order to increase the stability of an object,

1. The object’s centre of gravity should be as low as possible

2. The area of the object’s base should be as wide as possible

5) Relate and use the concept of stability to explain daily activities happening

in real-life context