[tag:classical-mechanics] entails the study of the trajectory of bodies under the influence of forces. More specific subtopics are: [tag:newtonian-mechanics], [tag:lagrangian-mechanics], [tag:hamiltonian-mechanics] for point particles and [tag:fluid-dynamics], [tag:statistical-mechanics] and ...
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1answer
145 views
What is actually a resonating vibration and resonance?
What is actually a resonating vibration and resonance?
I have searched many books and made Google search too but couldn't understand it clearly.
2
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2answers
102 views
Principle of Least Action via Finite-Difference Method
I have to be honest, the principle of least action seems to me more of a religious claim one takes on complete faith, though of course I'm hoping this is just because I don't understand it. I tried to ...
0
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0answers
17 views
What determines the motion in a Newton's craddle? [duplicate]
Let's say we have a Newton's cradle with five metal balls, each with a mass $m$. You pick up one and release it, and right before impact it has a velocity $v$. What determines weather the ball at the ...
6
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1answer
86 views
+50
Stability of rotation of a rectangular prism
I've noticed something curious about the rotation of a rectangular prism. If I take a box with height $\neq$ width $\neq$ depth and flip it into the air around different axes of rotation, some motions ...
1
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6answers
315 views
Centripetal Force Acceleration
Suppose you want to perform a uniform circular motion . Then a body performing uniform circular motion horizontally needs an acceleration $= \frac{v^2}{r}$ at each point on the circular path with ...
2
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1answer
49 views
Energy in a wind instrument?
My physics teacher said that he saw a guy playing a very large wind instrument on TV, and the guy apparently calculated that the total energy present in the instrument when he was playing was almost ...
-2
votes
2answers
50 views
Magnitude of force to keep stick in equilibrium
Problem statement
A straight and homogenous stick with mass m is pressed against a wall with the force F. The stick is horizontal perpendicular against the wall. Given that the friction between the ...
0
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1answer
31 views
Energy of a cylinder rolling down a path
Problem statement:
A cylinder rolls without slipping down a hill. It is released from height h. What is its speed when it come down? The cylinder mass may be completely concentrated on the radius R, ...
0
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2answers
122 views
Geometrical interpretation of complex eigenvectors in a system of differential equations
Let's consider a system of differential equations in the form
$$\dot{X} = M X$$
in two dimensions ($X = (x(t), y(t))$).
In the case that $M$ has real values, it is easy to give a geometric ...
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0answers
37 views
If Galileo had an electronic scale [closed]
If Galileo had an electronic scale, capable of absorbing the collision (without breaking) of 1 Kg sphere dropped from the top of Pisa tower what would had been the maximum measurement registered after ...
0
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0answers
26 views
Relation between the period of rotation and the period of revolution of a satellite
I read somewhere that the tidal forces between the earth and the moon causes the equality between the 2 periods of the moon and that every planet-satellite system will evolve to this condition (like ...
4
votes
2answers
815 views
Rigid body dynamics joints
I can't seem to find any info on connected rigid bodies by a joint. Can someone explain the basics to me? I'm trying to do a little research to find out how feasible it would be to implement 3d ...
5
votes
1answer
492 views
What are examples of classical physical systems having polynomial observables of degree greater than 2?
Specifically: What are empirically well-understood examples of (integrable) Hamiltonian systems whose Hamiltonians include polynomial expressions, in the canonical coordinates $\{q^i,p_i\mid ...
1
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1answer
64 views
6 Story Building Swaying, Normal?
Preface:
I'm currently sitting at my desk on a 5th floor in a South Florida office building, as I was earlier this morning when I felt the building sway slightly. It wasn't continuous and the ...
19
votes
3answers
346 views
How many points are required to make a black box
I have a black box with an arbitrary mass distribution inside it. I want to replace that object with n point masses without changing any mechanical properties of the box (center of mass, total mass, ...
3
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0answers
28 views
Is it possible to find a “replacement pendulum” for a system of two equal but perpendicular pendulums?
I ask this question, because at the end of this long day I'm just too dazed to derive the proofs myself (even though I know that I should feel ashamed for this).
So, the question:
Given two ...
0
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2answers
77 views
Stopping distance of two objects with equal Kinetic Energy
I'm working on a problem regarding two objects with the same kinetic energy.
Two objects with masses of $m_1$ and $m_2$ have the same kinetic energy are both moving to the right. The same constant ...
2
votes
0answers
67 views
Small unclarity in proof of Noether's Theorem
I'm trying to understand the proof of Noether's Theorem in my Classical Mechanics class. We formulated it as follows:
A continous symmetry is defined as a flow $\phi^{\lambda}(q(t))$ which leaves the ...
1
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1answer
111 views
Buoyancy Problem - Cubes in water
I have a tank with water (10 m high) , with an ideal seal at the bottom (water can't fall down, but can enter bodies).
I have a system of 6 cubes ( of polystyrene density= 20 Kg/m^3) with dimension ...
-2
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0answers
57 views
Need some help, physics degree [duplicate]
Ok, so I am currently finishing my physical science ASS Of Arts transfer= computer science or physics BA currently and am taking a break to learn all I can before I go back and finish. Physics has ...
1
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2answers
61 views
Classical/Quantum Coin Toss
I am having a brainfreeze moment and have confused myself, help appreciated!
Classical Coin: Heads OR tails.
Quantum Coin: Superposition Heads AND Tails.
Classical Mechanics: Deterministic (in ...
-2
votes
0answers
44 views
How can we feel, that something changes over time? [closed]
From the point of view of quantum mechanics the evolution of the universe is linear.
That is, if the vector is written as a sum of components, its evolution is described purely in terms of evolution ...
2
votes
2answers
98 views
Higher order covariant Lagrangian
I'm in search of examples of Lagrangian, which are at least second order in the derivatives and are covariant, preferable for field theories. Up to now I could only find first-order (such at ...
4
votes
1answer
100 views
Liouville's theorem and gravitationally deflected lightpaths
It is customary in gravitational lensing problems, to project both the background source and the deflecting mass (e.g. a background quasar, and a foreground galaxy acting as a lens) in a plane.
Then, ...
3
votes
2answers
78 views
Pendulum Wave Period
Recently I've seen various videos showing the pendulum wave effect. All of the videos which I have found have a pattern which repeats every $60\mathrm{s}$.
I am trying to work out the relationship ...
8
votes
2answers
448 views
Deriving the action and the Lagrangian for a free point particle in Special Relativity
My question relates to
Landau & Lifshitz, Classical Theory of Field, Chapter 2: Relativistic Mechanics, Paragraph 8: The principle of least action.
As stated there, to determine the action ...
6
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0answers
81 views
When does a PDE solve a variational problem? [migrated]
I understand that for a functional $J[f]$ on the space of differentiable functions $f$ on some domain, setting $\delta J[f]|_{f=f_0} = 0$ yields a (possibly nonlinear) partial differential equation in ...
1
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0answers
58 views
A quicker way to verify that a function is a constant of motion?
I have three particles that we can indicate with $\alpha$ ($\alpha$=0,1,2), they are identified by the $r^i_\alpha$ coordinates and $p^\beta_j$ conjugata momenta ($\beta=0,1,2$ and $i,j=1,2,3$).
I ...
4
votes
2answers
233 views
How do I show that there exists variational/action principle for a given classical system?
We see variational principles coming into play in different places such as Classical Mechanics (Hamilton's principle which gives rise to the Euler-Lagrange equations), Optics (in the form of Fermat's ...
0
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1answer
135 views
Do all black holes spin in the same direction?
My question is as stated above, do all black holes spin the same direction?
To my knowledge, the spin in the direction of the spin of the matter that created them. Another similar question was asked ...
1
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0answers
24 views
Hamiltonian system: match transformations and constants of motion
I have a problem about the interpretation of an exercise.
Given the following Hamiltonian
$$H=\frac{\mathbf{p_0}^2}{2m}+\frac{\mathbf{p_1}^2}{2m}+\frac{\mathbf{p_2}^2}{2m}-2V(\mathbf{r_1}- ...
-2
votes
2answers
81 views
acceleration due to gravity [closed]
From the picture we can evaluate the vertical and horizontal component:
Given on a book:
The figure above shows a small mass connected to a string, which is attached to a vertical post. If the ...
10
votes
3answers
370 views
Google interview riddle and scaling arguments
I am puzzled by a riddle to which I have been told the answer and I have loads of difficulties to believe in the result.
The riddle goes as follows:
"imagine you are shrunk to the size of a coin ...
2
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2answers
899 views
Dimensional Analysis: Buckingham Pi Theorem
I am studying for a fluids quiz and I am having a few problems relating to dimensional analysis but for the time being fundamentally I have a problem selecting the repeating variables. Like does ...
0
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2answers
58 views
Hamiltonian equations: can I divide a solution of motion for a constant?
I'm solving an exercise about Hamiltonian equations. I have followed the proceeding below. The results given by the book are different to mine because its first result is the half of mine (and the ...
0
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0answers
36 views
Dose the gravitational force produces precession in the spinning top?
I'm new at classical mechanics but the text book says there is the torque in the spinning top which generated only by gravitation. It is hard to explain the situation, I've add the link.
...
1
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1answer
91 views
Solving equation of motion of two massive particle exerting the gravitational force each other
I'm trying to analyze the motion of the particles which exert the gravitational force each other. Let $M_1$, $M_2$ be the masses of the particles, and the equation of motion of particle $M_1$
$$
...
22
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8answers
1k views
What is the Earth truly rotating about/revolving around?
Earth rotates on its axis and revolves around the sun, the sun revolves around the galaxy, the galaxy is also moving. So Earth's net rotation as observed from a fixed inertial frame consists of all ...
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votes
0answers
24 views
how to dot product in 3 dimensions? [closed]
i have two vectors, vector A = 12 and vector C = 15 . vector A makes 60 degrees clock-wise x-axis. vector C makes 45 degrees clockwise z-axis, 30 degrees counter-clockwise y-axis. i did not ...
-5
votes
1answer
72 views
0
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1answer
47 views
Addes mass forces: can a force depend on acceleration?
My friend and I had a little discussion about added mass forces.
I always interpreted "F=ma" as a cause-effect relationship, so I find rather uneasy to accept that the cause can instantaneously ...
0
votes
1answer
36 views
Kinetic rotational energy of a bar hooked to a coil
I have solved an exercise and I'd like to know if my proceeding about finding kinetic energy is correct or not, because this is the first time that I "meet" a situation like this.
"A bar has mass $M$ ...
0
votes
1answer
23 views
Doubt about coordinates and point of equilibrium
I'm solving an exercise about small oscillations and I have a doubt about coordinates that I have to use.
This is the text of the exercise:
"A bar has mass M and lenght l. Its extremity A is hooked ...
3
votes
3answers
264 views
When Hamiltonian and the total energy are the same
In which condition, the Hamiltonian is the same as the total energy of the system, or say $H=T+V$?
1
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1answer
40 views
A different proof for 6 degrees of freedom
I want a different proof of 6 degrees of freedom of a solid object made of $\ N$ particles. I am thinking along these lines:
Definition of rigid body is
$\ modulus[\vec{r_i}-\vec{r_j}]=constant \ ...
0
votes
2answers
63 views
Wave function interpretation $y(x,t) = (0.35m)\sin(10\pi t-3\pi x + \frac\pi{4})$
Wave function interpretation $y(x,t) = (0.35m)\sin(10\pi t-3\pi x + \frac\pi{4})$
I used to deal with function with one variable
And now theres are two, how can I interpret them?
Is $10\pi$ still ...
3
votes
1answer
66 views
When is classical mechanics valid for describing motion of atoms?
In Molecular Dynamics simulations, the Newton's equation of motion is used to calculate the time evolution of system. Once, I read in an introductory text that when the thermal de Broglie wavelength ...
3
votes
4answers
146 views
Can Newton's laws be explained by Quantum Physics? [duplicate]
I have only basic knowledge of physics.
Could you please explain to me if a "Quantum" laws can theoretically (perhaps in the future?) be used to explain everything in macro levels?
I'm having ...
0
votes
1answer
47 views
Something about collision [closed]
A sphere P of mass m, travelling with speed $u$, makes a head-on collision with a stationary sphere Q also of mass m. After the collision, the velocities of P and Q are $v_1$ and $v_2$ ...
2
votes
0answers
68 views
What happens when a ball stops bouncing?
If I were to drop a bouncy ball onto a surface, each successive bounce will be lower in height as energy is dissipated. Eventually, however, the ball will cease to bounce and will remain in contact ...
