Forces - Centre of Mass 02

The centre of mass is defined as a unique point in an object or system through which the entire mass of the object acts. This means that in physics, whatever the size, shape or complexity, an object can be treated as if it is a point mass. This actually makes any calculations that you do much easier than they would be otherwise. In a lot of regular objects like a rectangular block or a ball, the centre of mass is right in the middle. in regular objects that are not completely symmetrical, such as a tetrahedron, the centre of mass will still be inside the object but nearer the bottom than the top. In other objects, for example a rubber ring that you throw for a dog to fetch, it is actually outside of the object.

Finding the centre of mass for a regularly shaped object with a uniform density is easy, it can be done by drawing. Finding the centre of mass for other objects can be a little more tricky, for example, where is the centre of mass of a person? The answer there would be that it depends on the person. Children have a lower centre of mass than adults and it depends on how the weight is distributed round the body. The same applies to any object, for example, tall drinking glasses often are made with quite a thick base. That means more of the mass will be low down and so the glass will be less likely to fall over if it gets knocked accidentally.

The stability of an object depends on two things, the location of the centre of mass and turning forces. Let's take the example of a double decker bus. That is a tall vehicle so you might think that it would topple over easily. Not so, double decker buses need to be tipped over by more than 60 degrees before they get close to falling over. Do that to a fully loaded lorry carrying bales of hay and it would be on its side well before 60 degrees. But why?

The engine, gearbox and other mechanical parts of a bus are right down in the chassis. These have a much greater combined mass than the seats and body work so the centre of mass is also very low down and close to the centre line of the bus. As you try to tip a double decker onto its side, the pivot point is the wheels. The centre of gravity is off to one side of the pivot point so the force of gravity acting on the centre of mass creates a moment (turning force). This moment counteracts the tipping motion. If you keep tipping the bus further and further, at some point, the centre of mass will be directly above the wheels, theoretically, the bus would be balanced at this point. Further tilting of the bus would place the centre of mass outside of the line of the wheels so the turning force would then add to the tipping force and the bus would then fall on to its side. For the hay lorry, the centre of mass is much higher so it would not need tipping over as far as the bus before the centre of mass lies outside the wheels. It if for this reason that bridges are often closed to high sided lorries when it is windy.