In engineering, work is defined as any force creating the transformation or displacement of an object. Although displacement and force are both scalar quantities, work has no direction because of the nature of a vector product (or Dot Product) in mathematical equations. To give an example of what this means, consider the hydraulic fluid jumping from one level to another. We can view the work done to move fluid by looking at the two parts,
The first component, or force, is caused by the weight of the object. The second component, or displacement, is caused by the velocity vector of the fluid. In engineering, however, we usually don’t measure positions directly, but only velocities. That is, we know that if the fluid moves away from the observer, then the distance that it will travel will be less than the angle of attack between the observer and the part of the system that causes the change in velocity. And since the work done to change the position of the part by the velocity vector is also measured in units of velocity, we know that the work done is a scalar value.
The definition of work is actually a little more complicated than it seems at first glance. To understand how this works, we must first know what the normal function is. This is a definition used in calculus and other math courses. Basically, it says that the normal function defines a set of values that are tangent to the tangent of the function. Using this definition, we can define the amount of work done on any system through its angular velocity vector.
As the magnitude of the system increases, the angle of attack will decrease and the magnitude of the force that acts on the system will decrease as well. However, the value of the torque, which is the product of the force and the change in angle of attack, is still conserved. Work done on a system with a constant or small increase in its magnitude will always be a constant or small amount.
On the other hand, if the magnitude of the velocity changes as the system’s angle of attack changes, then the work done will change as the angle of attack changes as well. In this situation, however, the work done is a non-linear function of the change in velocity. In general terms, the term non-linear is used when the results of the function are not dependent on the initial condition. In an Angular velocity Correlation Analysis, a force f hits a system at some point and stays there for a time t while another system f runs from point A to point B. The difference in the values of the systems at points A and B is termed the Correlation Coefficient.
The main concept behind the Correlation Coefficient is that work done by a system is equal to the force that it repells. For instance, if you drop a bowling ball from the arm of an object, the force that it exerts against the bowling ball will be the same on every collision it encounters. However, the value of this force is different for the two objects. Thus, we can conclude that the location of the bowling ball determines where the force will be exerted on it and therefore, we can infer that the location of the bowling ball affects the value of the bowling ball’s torque.