Classical mechanics refers to the classical (i.e., non-relativistic, non-quantum) study of physics. Three major formulations of classical mechanics are Newtonian mechanics, Lagrangian mechanics, and Hamiltonian mechanics. The latter two are rather useful in extensions to Classical Mechanics; ...
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How can a photon have kinetic energy
Mass of a photon is 0 . And KE=1/2mv^2 . So if m=0 than how can a photon posses K.E.
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In what sense does variational calculus help us graph the path of a moving object represented by the stationary action formula? [on hold]
This is off the beaten path if you allow me to build a short history of the question.
Let us assume we have the function in hand we know that function will produce a stationary action so I assume if ...
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Gravity train solution through symmetries
I've been having trouble feeling okay with all of the solutions I've found to the Brachistochrone problem inside earth thus far. To me the way to do it is to show:
The time that it takes a path $\...
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1answer
41 views
Isn't Bohr's correspondence principle obvious?
I was taking an introductory course in quantum mechanics when I came across the Bohr's correspondence principle. According to Wikipedia, the correspondence principle states that the behavior of ...
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1answer
31 views
Does measured mechanical power and work change between inertial frames?
Imagine a car A is accelerating.
Two observers at constant speed, B and C, analyse the change of A's kinetic energy over a same time interval.
B sees A going from 10 to 30 m/s
C sees A going from ...
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16 views
Linear momentum based question [on hold]
The actual answer is 15km/s. So i think that taking astronauts in the system is incorrect as the astronauts and the spaceship have no common acceleration. So their reduction in weight would have no ...
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What is the point to ask a question that everyone knows the answers? [migrated]
I've asked the question twice, How central forces work? I gives examples of bodies that have determined position and a defined angular velocity. But these are questions from forbidden knowledge, no ...
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22 views
Time taken for an object to slide down a curved ramp (variable acceleration) [duplicate]
If given a ramp in the shape of a known function (which has a restricted domain so that the function is only decreasing), how can you find the time taken for an object to slide down that ramp.'
For ...
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1answer
16 views
How to work out mechanical advantage of different arrangements of hydraulic cylinders
I'm hoping you can help as I've having real trouble wrapping my beleaguered brain around this. If this question is better asked on another SE just let me know. Apologies if it's a bit pedestrian ;)
I'...
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0answers
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classical mechanics problem - three snails on an equilateral triangle [on hold]
This is a very classical problem in mechanics I received at an exam in my university. Three snails $A$,$B$ and $C$ are initialy located at the vertices of an equilateral triangle with side lenght $l$.
...
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3answers
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Why do things spin?
Let's say I have 2 boxes, one of mass M and one of mass 2M. They are separated by a distance of 1 meter. I drop them from the same height and see that due to the earth's gravity, they accelerate at ...
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Calculation of impulsive tension and velocity
Can anyone please help with the setup of a question.
Firstly, here is a similar question just to show the style of the solution expected:
And so the analysis continues.
So I am trying to set up a ...
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54 views
Can the Euler-Lagrange equation be used to derive the stationary action formula? [duplicate]
From what I understand I can use the Euler-Lagrange equation to find the function ( Let us call L. ) where L can be the function as stated in the action formula.
But how difficult is it to actually ...
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26 views
Lagrangian of Charged Particle Evaluated On-Shell
I am trying to calculate the Lagrangian of a charged particle in background gauge field evaluaed on-shell.
Let $A^{\mu}(x)$ be a gauge field. The action of a charged particle in this background gauge ...
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48 views
Classical Hamiltonian with Exponential Potential [on hold]
I'm trying to solving the following problem to prepare for an exam. Given the Hamiltonian
$$H = \frac{p_1^2}{2} + \frac{q_2^2 p_2^2}{2} + e^{-q_1 q_2 p_2}\ ,$$
(i) find two one-parameter families of ...
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28 views
Proofs of conservation laws [on hold]
See https://en.wikipedia.org/wiki/Conservation_law#Exact_laws for a list of conservation and approximation.
Also see https://physics.tutorvista.com/momentum/conservation-of-linear-momentum.html Law ...
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23 views
Is an infinite HCP lattice stable?
Nearest-neighbors are all equidistant in a hexagonal close-packed (HCP) lattice. Therefore, I was wondering, if I had an infinite HCP lattice composed of point (Coulomb) charges of the same sign (i.e. ...
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Find the acceleration time of a car [closed]
So given the power, mass, and distance of a car to travel i need to find out how long it will take.
Power is 84HP mass 200kg and distance is half a mile! I've tried my best and can't figure it out! ...
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2answers
24 views
Why does kinetic energy of elecron on Bohr's orbit not change if zero of potential energy changes?
If zero of potential energy is not taken at infinity, total energy and potential energy of electron change but not kinetic energy. Why is that so?
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1answer
27 views
Looking for a cheap, easy to find laser gain media? [closed]
So I want to make my own home made laser, but I'm having trouble deciding on what gain media to use. I'm not an expert on lasers but I know the basics of how they work from reading online.
I want to ...
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0answers
25 views
Angular momentum in merging stars
See taylor's classical mechanics page 302.
where $E=T+V=\frac{1}{2}m\dot{r}^2+\frac{l^2}{2mr^2}+U(r)$ thus for a two body problem with angular momentum $\neq 0$ the objects could never come close to $...
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3answers
38 views
A slipping cylinder comes into contact with friction
Suppose a cylinder is slipping rigidly on a frictionless horizontal surface. Then, at $t=0$ it reaches a different ground. The coefficient of friction between the cylinder and this new type of ground ...
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15answers
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When a balloon pops and lets a brick fall, where does the energy come from?
Let's say a scientist attaches a 1 kg brick to a large helium inflated balloon, lets the balloon go, and then it reaches an altitude of 10 000 meters before it pops, dropping the brick.
The brick ...
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0answers
15 views
Fluid Mechanics - The Maximum Flowrate of A Liquid Thourg a Pipe if There is Sudden Reduction in Diameter
Given a liquid (e.g water), flowing throug a pipe with D1, P1 and v1 as its diameter, gauge pressure and velocity respectively. If we then add a gate with smaller diameter d in the pipe without ...
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16 views
Normal force of a car driving over the crest of a hill
When a car is driving over the crest of a hill whose curvature is circular, its centripetal force is given by Fnet= mg-N
The equation implies that the normal force on the car must be smaller than the ...
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1answer
18 views
How to distinguish between applied forces and forces of constraint?
Is there any generic prescription to separate the set of applied forces to the set of forces of constraint with respect to any arbitrary physical system?
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2answers
395 views
What is the relation between a symmetry and the invariance of the Lagrangian?
While proving that homogeneity of space implies conservation of momentum, we use the fact that homogeneity of space means that the Lagrangian of the system remains invariant under translation. Why is ...
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2answers
73 views
The rail gun experiment revisited
A metal rod is closing a horizontal electric circuit as shown here. We apply a vertical magnetic induction $B$ as shown. The magnetic (Laplace) force on the rod is $F=I\ell B$ to the right. If $F$ is ...
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28 views
Gram Schmidt process in kinematics
Can the Gram Schmidt process help in solving kinematic questions by converting 2 dimensional motion in 1 dimension by finding projection vector on other vector?
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39 views
Damped harmonic oscillator
The book I am using to study classical mechanics refers to "characteristic time" of an over damped system. I don't quite understand what they mean by this. I know relaxation time of a underdamped ...
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2answers
75 views
Understanding Galilean Structure
I’m a student with a pure math background starting to work through Arnold’s “Mathematical Methods...” and I’m struggling right of the bat with Section 1.2 on Galilean Structure. (pg 4 - 6)
So we have ...
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1answer
80 views
A question over Liouville’s Theorem
I have some doubts about Liouville theorem, probably its just something conceptual.
So: I know that for a system in which Liouville’s theorem holds, the volume in the phase space is conserved.
But ...
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28 views
Electric and magnetic dipole selection rules in molecules
I don't know if this is a really elementary question to ask, but I'm trying to get a picture of how light interacts with a molecule with respect to optical/UV-visible transitions and the electric/...
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2answers
52 views
Can an accelerated spring in static equilibrium in its rest frame have different forces at each end?
Let's say I have two identical masses connected by a spring:
If F1 = F2 = F then the forces on either end of the spring are also F when the whole arrangement reaches static equilibrium.
Now if F2 >...
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1answer
38 views
Why equation of motion doesn't involve derivatives of power greater than 2? [duplicate]
The equation of linear motion in a given coordinate axis (say $x$) in my text book:
And throughout my mechanics course I never encountered derivative with power higher than 2 in EOM?
Why is it so?
...
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0answers
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What are the challenges of carbon nanotube aerogel sheets used in artificial muscles? [closed]
Since the features of carbon nanotubes look promising, I was wondering why carbon nanotubes are not yet used in commercial applications for artificial muscles.
What are the challenges that ...
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0answers
23 views
What effects of external interactions move the centre of mass of an object
If we have a closed system of two point masses and all of a sudden the the two particles exhibit equal linear accelerations in opposite directions due to some forces acting on them(like the case of an ...
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1answer
37 views
Water Bottle Condensation
My friends and I were at a party last night and we were crushing empty water bottles until the cap popped off and water vapor came out. I have two questions regarding this phenomenon. From previous ...
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1answer
60 views
Intuition for Hamilton-Jacobi equation derived from least action
I am trying to understand the Hamilton-Jacobi equation without the framework of the canonical transformations. Even on the case of a 1D free particle I'm getting stuck.
The system starts at fixed ...
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1answer
63 views
What is the name of this vector quantity that is similar to angular momentum?
Consider 2 identical circular disks, rotating with angular velocity $\omega$ and $-\omega$ respectively along the same axis. If we declare the mass of each disk to be $m$ and radius to be $r$ then the ...
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1answer
49 views
Derivation of Rotational Motion Equations using Calculus
How are the equations for rotational motion derived using calculus and the following general equations ?
$$\mathbf{v}(t) = \mathbf{v}_0+\int_{t_0}^t \mathbf{a}(t')dt'$$
$$\mathbf{r}(t) = \mathbf{r}...
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1answer
26 views
What physical properties determine the sound of a drum head?
I am working on a rubber substitute for a leather-membrane drum. The objective is to replicate to reasonable extent the "sound" or timbre that the leather drum head makes with a rubber drum head as ...
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0answers
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Newton-Hooke force and potential
The Newton plus Hooke force laws are unique between all the central forces:
They are conservative.
They produce a force o interaction that is reducible for a sphere to a point in the centre of the ...
2
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1answer
66 views
Help with Chrstoffel symbols for geometric mechanics problem?
I am working through the book Geometric Control of Mechanical Systems by Bullo and Lewis https://www.amazon.com/gp/product/0387221956/ and I am stuck on a problem, E4-18. The problem was evidently at ...
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0answers
33 views
Proof of holonomic constraints for a wheel on a track
I'm faceing a problem of a thin wheel of radius R rolling without slipping on a track (y = f(x); on xy-plan). The wheel plane stays vertical and tangent to the track at the contact point P. $\alpha$ ...
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1answer
20 views
Disparity in the equations of motion for a particle in a central field [duplicate]
Hello! I am considering the motion of particle in a central field and appear to derive inconsistent equations of motion when the Euler Lagrange equations are applied directly to (1) the Lagrangian $L(...
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2answers
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How do you solve classical mechanics problems with quantum mechanics?
Let's take the very simple problem of what happens if I drop a 1 kg ball from a height of 1 meter. Classically, $F = mg$ and $g \approx 10 \frac{\mathrm{m}}{\mathrm{s}^2}$, so the ball feels a force ...
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2answers
37 views
Reaction Force, Wall and Spheres
Two identical spheres with weights of 10N.
O and M is the center of the sphere.
Ropes are identical and have same length
Ropes are connected from point P.
How much newton is the reaction force (T) of ...
2
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1answer
79 views
Potential energy and conservation law
I'm preparing for my masters entrance exam on pure mathematics (thought some problems are devoted to classical/lagrangian mechanics). I would be grateful to clarify some basics regarding the ...
2
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1answer
53 views
Non-standing waves on string
My problem is the following:
Assuming, we have a string (homogeneous, no energy loss), with a given propagation speed: $c$.
Let the origin (the source) of wave at $x=0$, thus the incident (direct) ...
