Is \(\frac{\partial T}{\partial q} = 0\) Always True in Classical Mechanics?

In summary, the question is whether it is always true that the partial derivative of temperature (T) with respect to a generalized coordinate (q) is equal to 0. The conversation discusses the varying kinetic energy (T) of a system when a generalized coordinate (q) changes, and how this contradicts the claim that the derivative is always 0. An example is given using polar coordinates to further illustrate the contradiction.
  • #1
pardesi
339
0
is it necessarily true that we have
[tex]\frac{\partial T}{\partial q}=0[/tex]?
 
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  • #2
I imagine kinetic energy often varies if a generalized coordinate of the system varies. I don't see why that derivative would be 0 in general.

For instance, if the generalized coordinate q describes the angular velocity of a body about some axis, and q varies while holding all other generalized coordinates constant, then the kinetic energy T of the system varies, and that derivative is non-0... right?
 
  • #3
It's trivially not true for motion of one particle using polar coordinates (Goldstein, p. 26).

T=[itex]\frac{1}{2}m (\dot{r}^{2} + (r\dot{\theta})^{2})[/itex]
 
  • #4
exactly that was my point of contradiction to my profs claim
 

Related to Is \(\frac{\partial T}{\partial q} = 0\) Always True in Classical Mechanics?

1. What is classical mechanics?

Classical mechanics is a branch of physics that studies the motion of macroscopic objects under the influence of forces. It is based on the laws of motion and gravitation proposed by Isaac Newton and expanded upon by other scientists.

2. Why is there doubt in classical mechanics?

There is doubt in classical mechanics because of its inability to accurately describe the behavior of particles at the quantum level. Classical mechanics is limited in its ability to explain phenomena such as wave-particle duality and the uncertainty principle.

3. How does classical mechanics differ from quantum mechanics?

Classical mechanics relies on determinism, meaning that the behavior of a system can be predicted with absolute certainty. On the other hand, quantum mechanics introduces probability and uncertainty into the equations, making predictions more challenging.

4. Can classical mechanics and quantum mechanics be reconciled?

There have been attempts to reconcile classical mechanics and quantum mechanics, such as the development of classical limit theories. However, there is still ongoing debate and research on the compatibility of the two theories.

5. What are the practical applications of classical mechanics?

Classical mechanics has many practical applications in engineering, such as designing structures and machines, predicting the trajectory of projectiles, and understanding the behavior of fluids. It is also used in fields like astronomy and chemistry to model and predict the motion of celestial bodies and chemical reactions.

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