P3-1 : Moments
Trying to unscrew a nut requires a spanner. It is common knowledge that a longer spanner makes it easier – this is because less force is required to pull the nut out. Unscrewing a nut is an example of a turning effect. The turning effect of the force is called the moment, which can be increased by:
- increasing the size of the force
- using a longer instrument
You can work out the moment using this equation:
The diagram below shows a crowbar being used to lift a safe.
Imagine that someone is pushing down on that crowbar, and that is what causes the push. The push is the force applied by a person, which we call effort, when trying to lift objects – the load - around a pivot (the point at which the crowbar turns).
Centre of Mass
We say that there is a point of an object where we can think of it as though the weight acts at that single point. We call this the centre of mass or centre of gravity. The centre of mass is the point of an object where its mass may be concentrated.
For a symmetrical object, the centre of mass lies along the axis of symmetry. When an object has several axes of symmetry, it is where the lines meet.
A hanging object rests with its centre of mass directly below the point of suspension. This means that the object is said to be in equilibrium. Because the centre of mass is directly below the point of suspension, no turning effect is exerted by the weight, as shown with the left hanging flower basket. When an object is moved from its original position and released, it will swing back into its equilibrium position. This is because the weight of the object causes a turning effect on the object to move it back to that position, as shown with the right hanging flower basket. The point at which it is not in equilibrium is called non-equilibrium.
A moment in balance does not necessarily have to be with the pivot around the centre of the object. However, when balancing moments around an object we say they do. Look at the diagram below, showing a balanced moment:
Just by looking at the diagram you can tell the moment is in balance. You can also clearly see that the distances are different – which means that to be in balance, the weights bust also be different. Because it is in balance, we know that: W1 x D1 = W2 x D2.
This seesaw action is an example of the Principle of Moments. This states that for an object in equilibrium:
We can use (W1)(D1) = (W2)(D2) to do calculations involving moments. For example, if we are given the following diagram, where the pivot is not at the centre of mass:
We can calculate W0 if we know W1 and d1…