P3aL2 Moments and Stability

Key Words

Centre of mass - an imaginary point around which all the mass is thought to act.

Equilibrium - object is in balance; it is not toppling over.

Gravity - a pulling force between masses.

Neutral Equilibrium - object may roll, but not topple.

Resultant moment - the turning effect of all the forces.

Stability - how likely an object is to remain standing.

Stable - cannot be pushed over easily.

Stable equilibrium - object will return it is original position if pushed a bit.

Unstable - will tip over easily

Unstable equilibrium - how a force makes an object turn.

Grade E

A stable object does not tip over.  Objects that have a high stability do not tip over easily.  Their centre of mass is low down, near the base.  This candlestick has a low centre of mass so that it does not tip over so easily.

The candlestick is in stable equilibrium.  If you push the top, it will drop back to where it was.

Now suppose we put it upside down.

This time the centre of mass is high up.  It is in unstable equilibrium and if you pushed the candlestick, it would tip over easily.

Now we put it on its side:

If you push it, it will roll, but will not tip over.  It is in neutral equilibrium.

Grade C

We can find the centre of mass of an irregular object quite easily.  If we let it hang freely, the centre of mass is directly below where we hang it from.  We draw a line vertically downwards.

If we then hang the object from a couple of other points and draw the lines that go vertically downwards, the centre of mass is where the lines meet.

Let us look at how we can explain stability in objects.  This bus has a low centre of mass and a wide track (distance between the wheels)

You can see that there is a line of action of the weight that acts vertically downwards from the centre of mass.

If we tip the bus over:

The line of action of the weight is still acting vertically downwards, but one of the tyres is acting as a pivot.  There is an overall turning moment; in this case it's anticlockwise, so the bus will go back to the vertical.

Now suppose the bus tilts over further:

This time the line of action of the weight is to the outside of the tyre, so the turning moment is clockwise.  The bus tips over on its side.  (This has happened; a driver was late going off shift and was hurrying to get back to the garage.  Going too fast round a sharp bend, the bus tilted too much and tipped onto its side.)

Although they are tall, double-decker buses are very stable.  They test buses by putting lots of sandbags on the seats upstairs (with nothing downstairs) and tilt them over on a tilting platform.  The centre of mass is low enough to ensure that they are tilted to more than 60^o off the vertical before they tip over.

Grade A

Water slopping about in a ship can make it tip over.  Flooded car-decks on ferries have caused serious accidents where the ships have tipped on their sides with very little warning and major loss of life.

Life boats have a very low centre of mass so that they "right" themselves if they capsize.  The only stable position is the right way up.