Systems with Zero Torque
This page is a work in progress by Jake Baker.
Systems with Zero Torque
A Mathematical Model
It follows from the angular momentum principle, LAf = LAi + rnet*deltat that for systems with zero torque, LAf = LAi.
Examples
2.2 Middling
2.3 Difficult
Connectedness
This principle directly relates to the biomechanical techniques used by various types of athletes, it can thus for example be incorporated into a physical analysis of extreme sports. Athletes (figure skaters, skateboarders, etc.) are able to employ this principle to increase the rates of rotation of there bodies without having to generate any net force. Given that Ltot = Ltrans + Lrot, and assuming that a change in Ltrans is trivial, it follows that Lrotf = Lroti. More specifically ωfIf = ωiIi. This relation implies that the athlete in question should be able to either increase or reduce their angular velocity by decreasing or increasing his or her moment of inertia respectively. Generally, this is accomplished by voluntarily cutting the distance between bodily appendages and the athlete's center of mass. In the example of a figure skater for instance, the moment of inertia is decreased by bringing in the arms and legs closer to the center of the body. Additionally, the athlete might crouch down in order to further decrease the total distance from his or her body’s center of mass. As a result, an inversely proportional change in the angular velocity of the athlete’s motion will occur, causing the speed of the athletes rotation either increase or decrease.
As an LMC major, I am among the very few students at Georgia Tech for whom the zero-torque system method is not immediately applicable. If instead I was any sort of engineering major whatsoever, this would surely not be the case.
An immediate industrial example of a zero-torque system is alluded to in example problem two above. The zero-torque system is a very important method of abstraction in the field of control systems engineering. In particular, this perspective is instrumental for calculating selection factors for clutching and braking systems. Though often offered as separate components, their function are often combined into a single unit. When starting or stopping, they transfer energy between an output shaft and an input shaft through the point of contact. By considering the input shaft, output shaft and engagement mechanism as a closed system, researchers are enabled to make calculations that can inform them on how to engineer systems of progressively greater efficiency in regard to the mechanical advantage unique to different type of engagement system.
4 History 5 See also 5.1 Further reading 5.2 External links 6 References Main Idea[edit] Georg Ohm was a German who worked to discover a relationship between the potential difference across a resistor and the current. This was named after him, called Ohm's Law.
A Mathematical Model[edit] What are the mathematical equations that allow us to model this topic. For example dp⃗ dtsystem=F⃗ net where p is the momentum of the system and F is the net force from the surroundings.
A Computational Model[edit] How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript This page is a work in progress by Jake Baker Examples[edit] Be sure to show all steps in your solution and include diagrams whenever possible
Simple[edit] Middling[edit] Difficult[edit] Connectedness[edit] How is this topic connected to something that you are interested in? How is it connected to your major? Is there an interesting industrial application? History[edit] Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.
See also[edit] Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?
Further reading[edit] Books, Articles or other print media on this topic
External links[edit] Internet resources on this topic
References[edit] This section contains the the references you used while writing this page