Understanding Angles and Angular Momentum

For every action there is a reaction or in other words, if an object is doing work then there is a corresponding energy. A simple example of this is that the work which an object exerts on itself can be expressed by the formula E=mv where m is the mass of the object and v is its velocity. If the force applied to the object is constant then work can also be calculated by dividing the time of operation by the amount of the internal force acting on the object.

The work equation has a solution which can be derived by taking a look at it in the algebraic language. To do this, assume the original condition (i.e. the orientation of the work piece). Then find the components of this force i.e. the tangential force, the radial force, the horizontal pull of gravity acting on the work piece and the angle of attack. Find the values for these components in the direction normal to the x axis.

Next, we must solve for the angle of attack, which can be done by finding the integral of the sum of the vertical and horizontal displacements. This is done by finding the slope of the tangent plane to be equal to the integration symbol for the unit circle. The resultant of these two slopes is the horizontal displacement and is equal to the product of their differences. The function relating the horizontal displacement to the angle of attack is then found by adding the product of tangent planes that pass through the angle of attack and the z axis. This can be used to find the working displacement.

After finding the horizontal displacement, the next step is to find the resultant of this displacement, which can be done by dividing it by the cube of the original displacement to give the velocity. This velocity is the result of a constant velocity component acting upon the work piece being displaced. A constant velocity component will have zero values when the work piece is at rest or at its lowest position. This component, however, will have a magnitude that varies depending on the orientation of the displacement when the work piece is in motion.

This next step involves integration of this force vector with the other forces that make up the work piece. The integral of this force vector with the components of both tangent and curlwise forces acts as the derivative of the first term of this quadratic equation. When this quadratic equation is graphed, it shows a decrease in the magnitude of both the tangent and curlwise forces as the work piece moves toward the angle of attack. As the angle of attack increases, this component begins to decrease until it reaches a zero magnitude at the end of one complete revolution of the device.

This can be used to draw a force vector interior to the work piece. This component will act to increase the velocity of the work piece, as well as its angular momentum. This component is the integral that determines the orientation of a workpiece as it is moved through an angle of attack.