Pendulum - equipartition experiment

In summary, the problem concerns the conservation of energy and the concept of equipartition in thermal equilibrium. The total energy is equivalent to the conservation of energy, with one expression representing kinetic energy and the other representing potential energy. The degrees of freedom in this case are related to the rotation of the glass, with two degrees of freedom for both kinetic and potential energy. The equation for the mean total energy is Kbt, as each squared independent variable contributes 1/2 Kbt according to the equipartition theorem. In part c, the issue of obtaining the answer in radians or degrees without trigonometric functions is raised.
  • #1
ibysaiyan
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Homework Statement



The problem is : http://i44.tinypic.com/2v7yo29.png

Homework Equations


The Attempt at a Solution


For part a )
I have stated that: The total energy is equivalent to the conservation of energy i.e the two expressions obey the conservation principle. The expression dealing with inertia is the kinetic energy while the other expression's potential since this experiment can be analogous to a pendulum's oscillation.

b)
Now I know that equipartitions states that in thermal equlibirum each degrees of freedom contributes 1/2Kbt i.e for every squared term for the expression of the energy.
In the above case we have two squared expressions.. however i am a little confused with the degrees of freedom. The general mean equation is :
[tex]f/2 [itex]k_{b}[/itex]T ...

Would the mean total be 2/2 kbt since each expression gives one degrees of freedom.. Or I was thinking that since the glass can rotate in both direction ( clockwise and vice versa) so would that be 2 degrees of freedom for kinetic energy and 2 for potential as well ? :s

These are the only bits I am stuck on. Thanks for your expected replies!

EDIT: I think for part b the answer is simply Kbt since each squared independent variable provides 1/2 Kt according to the theorem. :yea =)
 
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  • #2
I am little stuck on part c... how can I get answer in radians or degrees.. if i don't have any trig. function ?
 
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  • #3
Anyone ?
 

1. What is the Pendulum - Equipartition Experiment?

The Pendulum - Equipartition Experiment is a scientific experiment used to study the behavior of a pendulum and its relationship to energy distribution, also known as "equipartition".

2. How does the Pendulum - Equipartition Experiment work?

In this experiment, a pendulum is set into motion and its energy is measured at different points along its swing. This energy is then compared to the theoretical predictions of equipartition, which states that energy should be evenly distributed among all possible forms.

3. What is the purpose of the Pendulum - Equipartition Experiment?

The purpose of this experiment is to test the principles of equipartition and to gain a better understanding of how energy is distributed and conserved in a system.

4. What are the key results of the Pendulum - Equipartition Experiment?

The key results of this experiment include the confirmation of the principle of equipartition, as well as the determination of the energy distribution in a pendulum system at different points in its swing.

5. How is the Pendulum - Equipartition Experiment used in scientific research?

The Pendulum - Equipartition Experiment is used in a variety of scientific fields, including thermodynamics, statistical mechanics, and quantum mechanics, to study the behavior of energy in different systems and to test theoretical predictions.

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