That is a good question Harry. I believe that under one circumstance all of the energy can be converted into heat, but that is very specific. A linear momentum case is an excellent one to use as the example. If an observer happens to be located on a reference frame that is at rest relative to the center of mass of the two ball closed system below, total conversion can be observed. In that case, the two balls must collide along their center axis and stick together. The final system would consist of two energy damaged balls at rest. The initial kinetic energy determined by the sum of the energy contained within each ball will be converted into some other form.
In that special case of total kinetic energy conversion, it should be noted that the linear momentum is conserved as required and interestingly, it remained zero. I am convinced now that this is a requirement if all of the kinetic energy is to be released. A similar conclusion could be drawn relative to angular energy and momentum. Dave -----Original Message----- From: H Veeder <[email protected]> To: vortex-l <[email protected]> Sent: Tue, Feb 11, 2014 12:11 pm Subject: Re: [Vo]:Energy and momentum / was RAR I think the rules imply it is true for both linear and angular momentum. No amount of the total momentum of a system can be converted into heat. However, some amount of the total energy of a system can be converted into heat. Is it possible to convert all of the energy into heat? Harry On Mon, Feb 10, 2014 at 10:59 PM, David Roberson <[email protected]> wrote: I do not see where we differ in understanding Bob. The system you describe had nearly zero total angular momentum before and after the collision so it remains conserved. The rotational energy can be extracted by various means as I also stated. Harry has concluded that angular momentum can not be converted into heat, which is always true. He also states that angular energy can be converted into other forms or energy including heat. Can you demonstrate a closed system where this is not the case? Dave -----Original Message----- From: Bob Cook <[email protected]> To: vortex-l <[email protected]> Sent: Mon, Feb 10, 2014 10:46 pm Subject: Re: [Vo]:Energy and momentum / was RAR Harry and Dave--Bob Cook here-- Keep in mind that the law is that angular momentum must be conserved. However systems with angular momentum can also have significant energy that can be changed to heat. Take two planets in the solar system with direction of rotation in opposite directions. One planet with a vector pointing to the North Star and other one with its vector pointing in a direction opposite to the North Star. They drift slowly together and eventually collide. If they have about equal mass and size and collide their total angular will approach zero. However there will be a lot of heat energy released. Angular momentum is a vector quantity--energy is a scalar with no direction attached. This holds for quantum systems with the Spin quantum angular momentum J associated with particles being a vector quantity. Electrons pair up to reduce their angular momentum to zero. Many quantum systems of particles tend to low spin states since low is consistent with the lowest energy state, and consistent with reactions that increase their entropy--the second law of thermodynamics. I think you two are forgetting the vector nature of angular momentum and mechanisms for its conservation. I do not agree with Harry's corollary. Bob ----- Original Message ----- From: David Roberson To: [email protected] Sent: Monday, February 10, 2014 6:19 PM Subject: Re: [Vo]:Energy and momentum / was RAR Your corollary would be an excellent addition to my discussion. Dave -----Original Message----- From: H Veeder <[email protected]> To: vortex-l <[email protected]> Sent: Mon, Feb 10, 2014 5:49 pm Subject: Re: [Vo]:Energy and momentum / was RAR On Sun, Feb 9, 2014 at 7:17 PM, David Roberson <[email protected]> wrote: OK. Energy is proportional to velocity squared. If you double the velocity, you have four times as much energy as in the first case. Also the direction of the motion is not important. For example, a ball moving to the right has a certain amount of energy and a second one moving to the left with the same mass and velocity will have the same amount as well. Energy adds, so you have two times the amount contained within one. Momentum is proportional to velocity directly. The direction of the movement is important since momentum is a vector quantity, unlike energy. The two ball case above results in a net momentum for the system of zero. The two vectors are equal and point in opposite directions so they cancel. Energy and momentum require different rules of behavior and can not be interchanged. Dave That is a good summary. As a corollary to the last statement, I would add that momentum cannot be turned into heat since heat is considered a form of energy. Harry
