All Questions
Tagged with momentum classical-mechanics
285
questions
-3
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1
answer
116
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Noether's theorem by a taste of logic [closed]
I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know - because physicists don't used to apply the method of "proof by contradiction". ...
- 1,409
-3
votes
2
answers
81
views
Meaning of $d\mathcal{L}=-H$ in analytical mechanics?
In Lagrangian mechanics the momentum is defined as:
$$p=\frac{\partial \mathcal{L}}{\partial \dot q}$$
Also we can define it as:
$$p=\frac{\partial S}{\partial q}$$
where $S$ is Hamilton's principal ...
- 443
0
votes
2
answers
82
views
Generalized momentum
I am studying Hamiltonian Mechanics and I was questioning about some laws of conservation:
in an isolate system, the Lagrangian $\mathcal{L}=\mathcal{L}(q,\dot q)$ is a function of the generalized ...
- 49
1
vote
0
answers
25
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Question about how force is distributed based on initial hitting angle in multiple pool balls
Suppose you have a standard triangle rack of billiard balls under ideal conditions (all balls are touching and identical, no friction, and all elastic collisions, ect). Suppose force F is applied to ...
- 11
0
votes
1
answer
69
views
Changing variables from $\dot{q}$ to $p$ in Lagrangian instead of Legendre Transformation
This question is motivated by a perceived incompleteness in the responses to this question, which asks why we can't just substitute $\dot{q}(p)$ into $L(q,\dot{q})$ to convert it to $L(q,p)$, which ...
- 7,398
1
vote
1
answer
42
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Elastic collision between 2 particles in 2D [closed]
A particle with mass $m_1=m$ moves along the x-axis at a velocity of $v_0$ and collides with another particle $m_2=4m$. As a result of the collision $m_1$ travels upwards at an angle of $90 ^\circ$. (...
- 111
1
vote
2
answers
80
views
Why isn't there such a thing as "internal momentum"?
The three most well-known conserved quantities in classical physics are energy, momentum, and angular momentum.
Suppose we have a system with no external forces acting on it. We can talk about the ...
- 8,640
1
vote
1
answer
65
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Landau/Lifshitz action as a function of coordinates [duplicate]
In Landau/Lifshitz' "Mechanics", $\S43$, 3ed, the authors consider the action of a mechanical system as a function of its final time $t$ and its final position $q$. They consider paths ...
- 349
1
vote
1
answer
49
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Definition of generalized momenta in analytical mechanics
I've seen mainly two definitions of generalized momenta, $p_k$, and I wasn't sure which one is always true/ the correct one:
$$p_k\equiv\dfrac{\partial\mathcal T}{\partial \dot q_k}\text{ and }p_k\...
- 296
1
vote
1
answer
54
views
Sufficient condition for conservation of conjugate momentum
Is the following statement true?
If $\frac{\partial \dot{q}}{\partial q}=0$, then the conjugate momentum $p_q$ is conserved.
We know that conjugate momentum of $q$ is conserved if $\frac{\partial L}{\...
- 41
1
vote
0
answers
28
views
Angular momentum along a straight line with 2d velocity
I have a stationary referance for $L = 0$, $L = \vec{r} \times m\vec{v}$ can be interpreted as an area of a paralelogram. The area is constant, since $base \times height = constant$.
However, is this ...
- 21
0
votes
0
answers
74
views
Conversion of cartesian momenta to generalized ones
The cartesian kinetic energy for a particle in $\mathbf R^3$ is
$$\mathcal T=\dfrac{1}{2}m||\mathbf x||^2=\dfrac{1}{2}m(\dot x^2+\dot y^2+\dot z^2).$$
Knowing that momentum conjugate to $\square$ is
$$...
- 296
-4
votes
3
answers
80
views
How do you prove the formula for momentum? [closed]
I am just an absolute beginner to physics. I've seen a proof of the formula for momentum using Newton's second law of motion, but to prove Newton's second law of motion you have to use the formula for ...
0
votes
3
answers
56
views
What is the meaning force averaged over a long time?
There was problem in my high school test which says,
There is a ball of mass $m$ between two walls (seperated at a distance $d$) moving with speed $v$. The collision of ball with the walls is ...
- 242
0
votes
1
answer
80
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Lagrangian and Hamiltonian Mechanics: Conjugate Momentum
I am a physics undergraduate student currently taking a classical mechanics course, and I am not able to understand what conjugate/canonical momentum is (physically). It is sometimes equal to the ...
