LESSON 4: Moments


Another main idea of statics is the concept of moments. In this section we will talk about moments around a point. A moment is simply a rotation. Observe this example of a bar connected by a pin joint:


As you can see, the upward force (red arrow) causes the bar to spin around the pin joint. This is called a moment about a point. Remember the word “static” means still, and a key part of keeping something still is to keep it from rotating. This brings us to another main rule of statics: The sum of the moments about a point must equal zero. This simply means that all the forces on an object must be positioned in such a way that the object will not spin.



Every moment has a value, for example, some moments are stronger than others; an object can spin quickly with a lot of force or slowly with a small amount of force. The way to find this value is: (perpendicular distance) x (force of vector) = force of moment.
Observe the diagram to the left, where the red vector has a magnitude of 10 N and is located a perpendicular distance of 5 meters away from the pin joint. This red vector creates a moment of 50 Nm ( 5m x 10 N = 50 Nm) about the pin joint. It is important to note that you must always use the perpendicular distance to find the moment. This concept of perpendicular distance will be further explored in the next section.



In this example our goal is to find the magnitudes of the two green vectors in order to keep this bar static. We will begin by summing the forces in the y-direction. Remembering from previous sections that the forces going up must equal the forces going down, we know that the two green vectors must add together to equal the red arrow ( 10 N) .
From the current section we know that the sum of the moments about a point must equal zero. We know that the red arrow creates a moment of 50 Nm in the counterclockwise direction, so the two green arrows together must create a moment of 50 Nm in the clockwise direction. We now have two equations and two unknown variables. Solving these two equations yields: A? (the green vector closest to the pin joint) = 4N and B? (the green vector furthest from the pin joint)= 6 N .