Turning Effect
Suppose that you try to balance a ruler on your finger, but the centre of gravity C is not directly above your finger. The ruler would lose its balance and fall to one side.
When the ruler falls to one side, it is rotating. This happens because as the weight pulls the ruler downwards at C, you finger pushes the ruler upwards at another point. The two forces are not along the same straight line. This gives a turning effect. If these two forces are equal and opposite, then the pair is called a couple.
When two equal and opposite forces at on a body, it is easy to think that they cancel and the body could stay at rest. However, for a large body like the ruler, it can happen that the two forces are not acting along the same straight line. If so, the the body would not be at rest even if the forces are equal and opposite. As we have seen above, the body would rotate. So we must be careful not to think that of we have two equal and opposite forces acting on a body, the body must be at rest, or the forces must be in equilibrium. This is only true when they act along the same straight line. This means that:
For the forces acting on a body to be in equilibrium, both the resultant force and the resultant couple must be zero.
This applies to any number of forces. Suppose we are given two forces and we need to determine if they are in equilibrium. First, we must check if the resultant force is zero. If the forces are equal and opposite, then it is. Next, we must check if the resultant couple is zero. How do we find the couple in the first place? Finding the couple for any number of forces is tricky. We shall only look at two simple cases here.
The first case is when there are only two forces and they are equal and opposite, like what we have here. Then the couple is given by:
The second case is when the forces all lie in the same plane, and the resultant force is zero. Then the resultant couple is equal to the total moment of the forces. So, for the forces to be in equilibrium, the total moment must be zero. The more common way to express this is the principle of moments:
I shall explain this in more details in the page on
principle of moments.
Copyright 2011 by Kai Hock. All rights reserved.
Last updated: 16 March 2011