An object is stable if it is difficult to knock over. A stable object will tend to return to its original position when disturbed.
The stability of a system is connected to its equilibrium state (the state where there are no net forces acting - all are balanced). There are three types of equilibrium that can be used to descibe a system:
If a system in stable equilibrium is disturbed slightly, then it tends to return to its original equilibrium state. It usually oscillates around that state first but eventually settles down in exactly the same position as it started at. It does this because its centre of gravity is already at the lowest possible position.
An unstable system moves away from its original equilibrium state when disturbed. It is not easy to return it to the original equilibrium position. It wants to move away from the original position as soon as you disturnb it. It does this because its centre of gravity is high up and when distrubed the centre of gravity continues to move to a lower position (a more stable one).
A neutral system is one where the centre of gravity of the system is always at the same level. If you distrub it slightly it will therefore settle in the new position with out a need to move further on or to move back.
Here is a VidClip about the stability of a vase
The centre of gravity of the funnel is high up - it will be at the middle of the mass - and as most of the mass is in the funnel end it will be up above the middle of its height when it is standing like this.
You only have to tip the funnel a little way for the line of action of the weight (the weight arrow) to fall outside the base and produce a turning moment. The funnel will therefore tip over easily.
The centre of gravity of the funnel is now low down - it will be at the middle of the mass - and as most of the mass is in the funnel end it will be low down when the funnel is in this position. For the funnel to tip over the line of action of the weight force arrow will have to form a clockwise moment. You have to push it a lot for that to happen
Note that when the funnel is standing on the wide base area it has to be tipped a long way before its equilibrium position shifts. That is because the base is wide and the centre of gravity is low.
When a funnel is lying horizontally on its side at rest on a table, it is in a state of neutral equilibrium. This is because a small displacement will cause the funnel to roll (and it will not return to its original position) but the position of its center of gravity will remain unchanged.
When the funnel is standing on the wide base it is in stable equilibrium because its centre of gravity is low and its base is wide. you would have to tip it by a big angle before it would not topple back to its original position.
When the funnel is standing on its neck opening it is in unstable equilibrium. You would only have to tip it by a small angle to make its high centre of gravity vertically above a point outside its base. It is therefore easy to topple over!
If you want to stay stable you need to keep your centre of gravity vertically above the area you are balancing on - whether that is on two feet, one foot or one finger! If you do not do that you will topple over!
Sometimes things behave in a way that seems very strange - but if we think about it carefully and look at the construction of the objects we can work out why they behave in that way.
...and here are some more demos....
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