Questions tagged [conservation-laws]
The statement that a property of a system does not change if the system is isolated.
3,146
questions
1
vote
3
answers
74
views
Conservation of linear vs. angular momentum in two similar cases
I have a question that eludes my understanding:
Imagine we have a bullet of mass $m$ and a rigid pendulum with a bob of mass $M$ hanging from a rigid rod of negligible mass hanging from the ceiling ...
- 12.4k
2
votes
3
answers
192
views
Two contradictory derivations of Killing equation
In David Tongs lecture notes he derives the Killing equation by showing that the charge $Q=\xi_\mu \frac{\mathrm{d}x^\mu}{\mathrm{d}\tau}$ is conserved
$$ 0=\frac{\mathrm{d}Q}{\mathrm{d}\tau}=\frac{\...
- 73.8k
0
votes
1
answer
741
views
Conservation of momentum of airplane in runway
On exercise 4.6 from Klepper's Book "Intro do mechanics" there is a plane on a landing lane. It has its engine off but is braking with force $F_b$. Also, it is attachted to a sandbag that ...
- 1
10
votes
2
answers
940
views
Conservation of Komar mass
The definition of Komar mass in GR is associated with one asymptotically flat end. However, a hypersurface may contain more than one end, such as the spacelike Einstein-Rosen bridge in Kruskal ...
CommunityBot
- 1
1
vote
2
answers
147
views
Doubt on conservation of angular momentum for Kepler's laws
Just before proving Kepler's laws, my Professor claimed that if $\vec{F}$ is a central force with center $O$ and it is the only force acting on a point $P$, then the trajectory of $P$ is a curve plane....
- 13
2
votes
1
answer
434
views
Komar Charge Derivation from Killing Current
We can define a divergence-less current from any Killing vector field $\xi^a$ by
$$ J^a[\xi] = \xi_b R^{a b}$$
I would like to show that
\begin{equation}\star J = \mathrm{d}\star\mathrm{d} \xi.\...
CommunityBot
- 1
1
vote
2
answers
722
views
Kinetic energy produced in an explosion
If there is a train moving at 2 m/s with a cannon attached to it loaded with a ball, and then the ball is launched from the train, how would one find the kinetic energy produced by the explosion if ...
CommunityBot
- 1
0
votes
0
answers
39
views
Idealized Newton's cradle
I was wondering about the conditions for an ideal newtons cradle.
Under regular circumstances, the collisions are inelastic and a newton's cradle dissipates energy in various forms like heat, friction,...
- 207k
1
vote
0
answers
62
views
Apparent violation of Newton's Third Law in relativistic force transformation
In special relativity, we know that, relativistic force is defined as F = dp/dt, where p = γmv.
For forces perpendicular to the direction of relative motion, force transforms as F' = γF.
Consider two ...
- 207k
1
vote
2
answers
63
views
Which kinds of systems are described by a heat equation?
Every extensive thermodynamic variable has a continuity equation associated to it:
$$\frac{\partial \rho}{\partial t}+\vec \nabla \cdot \vec J=0$$
where $\rho$ is the density of said variable and $\...
- 38.3k
2
votes
1
answer
19k
views
How do I derive the formula of coefficient of restitution?
I have learnt in collision mechanics about the term "coefficient of restitution":
$$e=\frac{v_{2,\text{f}}-v_{1,\text{f}}}{v_{1,\text{i}}-v_{2,\text{i}}}.$$
But the sad part is that my book ...
CommunityBot
- 1
1
vote
3
answers
344
views
Conservation of linear momentum after explosion with friction
Let's say you have a bomb at rest submerged in a liquid. It then explodes into two equal fragments A and B which leave in opposite directions.
If we ignore the fluid and any sound or light we can ...
CommunityBot
- 1
0
votes
2
answers
154
views
Is there any phenomenon where opposite reaction (Newton's 3rd Law) is not fulfilled?
I'm wondering if there is any case in nature/physics where it has been observed "where there is an action, there is not necessarily an exact equal and opposite reaction".
Or is there some ...
- 207k
-3
votes
1
answer
116
views
Noether's theorem by a taste of logic [closed]
I am a mathematician and I asked this question briefly and my question became closed, may be - I don't know - because physicists don't used to apply the method of "proof by contradiction". ...
- 1,897
2
votes
1
answer
265
views
Heat transfer direction in fins
I'm unsure of what exactly is changing the heat transfer direction in the following triangular fin:
$$
q_{x} = -kA(x)\frac{\mathrm{d}T(x)}{\mathrm{d}x}
\tag{1}
$$
$$
\begin{align}
q_{x+\mathrm{d}x} &...
CommunityBot
- 1