# Tag Info

### In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?

The notation is a little sloppy from a purely mathematical point of view (although common in physics) so it might be causing a little confusion. To help clarify, it might help to use different letters ...
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### In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?

They are partial derivatives. From the chain rule, we have $$\frac{\partial V(aq_1-bq_2)}{\partial q_1}= a V'(aq_1-bq_2),\\ \frac{\partial V(aq_1-bq_2)}{\partial q_2}= -b V'(aq_1-bq_2).$$ For ...
• 54.5k
Accepted

### Total differential of internal energy $U$ in terms of $p$ and $T$ using first law of thermodynamics in Fermi's Thermodynamics

Fermi was probably the last physicist who excelled as a theoretician and an experimentalist. His lectures inspired many students, who became outstanding physicists in turn. His textbook on ...

### How do you differentiate $F^{αβ}$ with respect to $g_{μν}$?

If you are going to differentiate $L$ with the respect to the metric, $L$ needs to be rewritten without the metric being implicitly used anywhere. Otherwise, you will not vary the entire dependence on ...
Accepted

### Transformation to replace a Material derivative with a spatial derivative

In the technical paper referenced below, Gringarten et al. claim... $$\rho c \Bigg[ \frac{\partial T(z,t)}{\partial t}+v\frac{\partial T(z,t)}{\partial z}\Bigg]=Q(t)$$ can be reduced with the ...
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### In equation (3) from lecture 7 in Leonard Susskind’s ‘Classical Mechanics’, should the derivatives be partial?

No. The notation means that the V on the RHS is a function only of one variable, and so its derivative is the simplest, one-variable derivative.
Accepted

1 vote
Accepted

### Why is $(\partial_\mu F_{\alpha\beta})F^{\alpha\beta}=F_{\alpha\beta}\partial_\mu(F^{\alpha\beta})$?

Here the solution asserts that this is equal to simply equal to twice the first part of the term, implying $(\partial_\mu F_{\alpha\beta})F^{\alpha\beta}=F_{\alpha\beta}\partial_\mu(F^{\alpha\beta})$. ...
• 21.9k
1 vote

### What's the difference? $\nabla_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~\text{ and }~\partial_\mu e_\nu=\Gamma_{\mu \nu}^\rho e_\rho~?$

The expression $\partial_\mu \mathbf{e}_\nu$, at face value, does not really make sense in curved space due to the vectors being in different tangent spaces. In order to make it work, vectors need to ...
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1 vote

### Does (covariant) divergence-freeness of the stress-energy tensor ${T^{\mu\nu}}_{;\nu}=0$ follow from the Bianchi identity?

The law of local conservation of $T$ is consequence of the law of motion of the matter part of the total action matter + curvature $$I[g]+ J[\phi, g]$$ These equations of motion for the matter arise ...
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1 vote

### The conservative force

While @basics has the math right, I understand your question is about the physical interptetation. To answer this, we must understand what a force field is, since the definition of the rotation ...
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1 vote

### The conservative force

An example might be the best way to see it. Set up some electrodes that create a horizontal electric field. Make it so the field strength is proportional to height. This is a non-conservative field. ...
• 41.1k
1 vote

### The conservative force

Remark the curl it's the measure of the rotation of the vector field around a specific point Before answering your question, I'd replace (local) "rotation" with (local, or elementary) &...
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