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16 votes
Accepted

Areas with anti-parallel gravity in classical physics

If we let the $y$-axis point upwards then OP's 2D gravitational field is $$\vec{g}~=~ \begin{pmatrix} 0 \cr g~{\rm sgn}(x)\end{pmatrix}.$$ It has a non-zero curl $$(\vec{\nabla}\times \vec{g})_z~=~2g\...
Qmechanic's user avatar
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6 votes

Does a rocket moving in a circle expel exhaust at a greater velocity?

This is an interesting question, because when it is moving in a circle, the magnitude of its tangential velocity is constant and its angular velocity is also constant. Therefore the total kinetic ...
KDP's user avatar
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6 votes
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Is it possible to understand in simple terms what a Symplectic Structure is?

At the most rough level possible, a symplectic structure (geometrically) is an even-dimensional manifold together with a preferred choice of two-dimensional planes which, taken together, span the ...
11zaq's user avatar
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5 votes

Areas with anti-parallel gravity in classical physics

The potential that yields your provided force field is discontinuous. One possible choice would be $$V(x,y) = \begin{cases} gy & x\leq 0 \\ -gy & x>0 \end{cases},$$ which has a dicontinuity ...
Refik Mansuroglu's user avatar
3 votes

Does a rocket moving in a circle expel exhaust at a greater velocity?

The energy of the fuel does become the kinetic energy of the exhaust. Let us ignore the fact that the rocket becomes lighter as it burns fuel, and that it will eventually run out of fuel. The rocket ...
mmesser314's user avatar
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2 votes
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Question regarding gravitational force as external force

My doubt is if gravitational force is considered as an external force Yes, it is considered as an external force, an external conservative force. ...so how come can we apply Total mechanical energy ...
hft's user avatar
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1 vote

In the flow equation in Lecture 9 from Susskind’s ‘Classical Mechanics’, why is there a negative sign? Why is there partial and regular derivatives?

He says that if the flow velocity $v_x$ in the $x$ direction varies across the box, then the net flow into the box in the $x$ direction (across two faces) will be proportional to $-\frac{\partial v_x}{...
hft's user avatar
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1 vote

Equilibrium in physics

In short, it has to do with dissipation. I will start with a very qualitative answer. A classical pendulum (or oscillator) does not exchange energy/heat with the environment so it is "stuck" ...
JalfredP's user avatar
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