Statics

Alright, so when we talk about Statics it is all about being stationary. What is stationary? most of the time a rigid body which is not moving, is stationary. Does that mean there is no force applied to it? How about the weight of body? That's a force right there! So there is a force applied to it. Therefore, stationary means the overall forces that are applied to it are in equilibrium. That is, all the forces are in balance with each other and neutralize each other so that the body is static. If the forces were not in balance, then the rigid body will be in motion which has its own physics explained in Dynamics. One should also know that this type of force that sets motion is an external force. There are also internal forces that keeps the parts of a body together. 

Weight of a body is a force. A force is a pull or push that is applied to a body, so the weight of a person is a force that is applied to the body of that person through gravity of earth. That is a gravitational force. Similarly, there are other types of forces such as electrostatic, magnetic, etc.

If we want to represent a force in mathematics and make it more sensible we can say it is a vector that has a direction, a point of application, and a magnitude. Forces in mathematical format are shown as a multiplication of unit vector and magnitude. A unit vector has a unit length in the direction of a coordinate axis (i, j, and k). There fore it is easy to show the vector of force by using the unit vector and a value such as F = 2i + 3j. This was a two-dimensional example, meaning that is is in the x-y coordinate system utilizing the x and y unit vectors. The force is comprised of 2 unit in the direction of x-axis and 3 units in the direction of y-axis. As a result of these two components of the force we will have a resultant or the sum of the two component that shows the actual direction and magnitude of the force. Similarly, if there is several forces applied to an object in different directions, there is a resultant or sum of all those forces that makes the one force with a certain magnitude and direction applied to that object. Now if that resultant equals zero, then the object is static and not in motion, and if not, it will move. Here is a link that shows the concepts in graphics (accessed 05/11/2015). 

Similarly, when we have a force presented in 2D or 3D dimension, we can find the components of that force in the x, y, and z directions by using its angle cosines with respect to each direction. This link may be of more help understanding it (accessed 05/11/2015). This operation is called resolution of force. 

Next, is the concepts of moments or torques. When you try top open the lid of a jar of jam, you are applying a moment to the lid. That is, a moment is a force that results in a twist or rotation of a rigid body. Whenever we have a moment, we also have a pivot point (o), around which the rotation occurs. The vector from the pivot point to the point of application of the force is called position vector (r).  However, this whole rotation of the body as a result of the moment happens if the body is not restrained, but that doesn't mean there will not be any moment or torque applied to the object. There is a moment applied when you try to open the lid, but if it is restrained enough, the moment you applied is not able to rotate it. The magnitude of a moment is counted by the multiplication of the force applied times the moment arm length, and therefore, the units are in the form of length × force such as inch-pounds and newton-meters.  Moments are also shown as vectors. A moment about the pivot point is shown as the cross product of the force and the position vector: 

M (around point o)  = r × F. The distance between the pivot point and the point of force application is called the moment arm (d). Take a look at the picture on this page or this page (accessed 05/11/2015). What is nice to know about the direction of moments is the right-hand rule which is to show the direction of the moment in graphics: 

• 1. Point your index finger in the direction of position vector

  2. Point your middle finger in the direction of force vector

  3. The direction of your extended thumb shows the direction of the moment.

The right hand rule is also used in electrostatics to determine the direction of current and electromagnetic fields. You may check out this link for a graphical example (accessed 05/11/2015). The component of the moment about each coordinate axis can be found using the cosine of the angle that the force makes with that axis and multiply it by the magnitude of the moment. For example, Mx = M × Cos(θx)

Next, we have the concept of couples, which is a pair of two equal forces applied in parallel directions but opposite from each other, that act like a double moment over a pivot point. A couple is shown by a single moment vector as it is like the two forces create one torque all together. Only another couple can counteract a couple. A free moment, or a moment of couples is a moment that can be transferred to any other location without affecting the equilibrium requirements. Here is a page with graphical explanations on couples (accessed 05/11/2015).

In order to be able to answer the static questions of FE exam, we need to learn a little more about the stationary state of the objects and understand different conditions of equilibrium. So what happens if there are several different types of forces applied to an object. How to keep it static? This takes us into the subject of System of Forces.