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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Why do very small balls attached to a tiny spring propel themselves in hardly moving fluids? [duplicate]

I recall watching a youtube video about a ball with a spring on the idea propelling themselves through stable fluids without any assistance, even if we make sure the spring isn't moving in the ...
5
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0answers
472 views

Hamiltonian function for classical hard-sphere elastic collision

I'm trying to find the Hamiltonian function for a system consisting of a single particle in one dimension colliding elastically with a wall at $x = 0$. Everything I've read on the topic (e.g. this ...
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2answers
52 views

Deriving Hamilton's equation of motion

I am trying to derive Hamilton's equations of motion without using Lagrange's method but am left with an additional factor of $1/2$. Where am I going wrong? Please note this in not a homework ...
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2answers
146 views

How to reconstruct the dependence of the potential from a coordinate?

An ion moves along the x-axis of a black box with a speed $V$ and returns in a time $$T=a V^b$$ where $a$ and $b$ are some known constants. Having this, can we reproduce the dependence of a field ...
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1answer
26 views

Are there fifth-kind and sixth-kind generating functions?

In Goldstein's Classical Mechanics (2nd ed.), Section 9-1, pgs. 382-385, the generating functions (hereafter denoted $F$) for canonical transformations are introduced. From here on out, I'll refer to ...
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42 views

Independent canonical coordinate variables?

In Goldstein's Classical Mechanics (2nd ed.) on section 9-1 page 382, there is a discussion about finding a canonical transformation $(q_i,p_i)\rightarrow (Q_j(q_i,p_i,t),P_j(q_i,p_i,t))$ from a given ...
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28 views

Which of Landau's books are suited for undergraduates? [closed]

Seeing how well-received Landau's books are, I want to know if any of them are suited for undergraduates.
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4answers
204 views

Forces Create Angular Acceleration And “Straight” Acceleration - But How Much Of Each?

Let me set up the following problem for a rectangle floating in space: We know its dimensions. We know its mass. There's a force pushing it for a known amount of time - we know the angle & ...
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2answers
65 views

What causes the balloon to pop when we push with needle onto it's surface?

I am a bit puzzled because I can see two possible reasons, first one is more common and the other one makes sense too, so here they go: 1) balloon pops because of the fact that after pressure is ...
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2answers
161 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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0answers
14 views

Ski treadmill materials

This ski treadmill is not much of an incline, but it still allows people to ski and carve out turns. What materials have such a low coefficient of friction, yet allow higher friction at higher ...
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1answer
48 views

hard sphere collision condition with periodic boundary conditions

Hello Stack Exchange Physics, I am curious if there is an analytical or efficient numerical solution for the collision of hard spheres in a rectangular unit cell with periodic boundary conditions. ...
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1answer
29 views

When an object is moving at a constant velocity,would the normal force and $mg$ be equal?

Does the object's normal force and $mg$ cancel out, resulting in the two force becoming equal, or would one force be greater than the other? Thank you! Edit: Also would the $mg$ be considered weight ...
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2answers
74 views

Minimum initial vertical velocity of a projectile

A basketball is launched by a person with an initial velocity $v$ at an angle $\theta $ from a height $L$ into a basket of height $H>L$ which is a horizontal distance $d$ from the person. ...
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0answers
17 views

Relation between solvent accessibility and brownian motion

Assume one has a molecule (made of nodes) inside a solvent. If one tries to model the average effect of the interaction between the molecule and the solvent, one has two effects: 1- Friction term on ...
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4answers
3k views

Hamiltonian is conserved, but is not the total mechanical energy

I wondering about the interpretation for the energy difference between the Hamiltonian and the total mechanical energy for systems where the Hamiltonian is conserved, but it is not equal to the total ...
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0answers
19 views

Probability of light being refracted in deep space by H 2(Hydrogen)

Is it a valid question to ask what is the percentage of light that gets refracted by H 2 for a certain distance(Lets say 1 light year) in deep space. Lets assume a few(3) Hydrogen atoms per cubic ...
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2answers
264 views

Clearing up confusion about calculating torque

Suppose you have a shape consisting of two perpendicular rods (the whole shape is a rigid body) which stands upright so the plane of the rods is perpendicular to the plane of the ground, and the ...
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0answers
34 views

When the equations of motion are not unique (eg. when they are given by eigenvectors), which will the free particle adhere to?

For this question I think it will be easier to express the usual equation describing the motion of a "free particle,"--viz. $g_{ij}\dot{x}^i\dot{x}^j$--in matrix form as follows: ...
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1answer
54 views

Is there really no transverse sound wave in air? [duplicate]

Everything has some viscosity. The viscosity of the medium may support transverse wave, right? So, is there really no transverse sound wave in air?
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3answers
120 views

How much energy does it take to simply run forward?

I'm interested in tracking as much data about my runs as I can in an effort to get faster, and while I can easily estimate energy expenditure during an uphill run due to the change in elevation, I ...
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4answers
53 views

Detached wheel from a moving vehicle speed

If a wheel is detached from a moving vehicle, would it speed be higher than the vehicle? Why?
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0answers
31 views

Maximum possible acceleration value on a ball in volleyball game

I have been examining this subject on web but could found enough information yet. I have to make a decision on choosing "range" for accelerometer which will measure acceleration value of ball in ...
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1answer
42 views

Experiment: releasing the copper bar above a permanent magnet

A classic experiment shows that when we drop a magnet through a copper coil long tube, there is eddy current induced in the coil. Then, due to lenz law, the motion of the magnet will be opposed and it ...
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4answers
324 views

How to prove that any rotation can be represented by 3 Euler angles

How can one prove that any rotation of a rigid object in 3-dimensional (3D) space can be represented by a sequence of three rotations around pre-fixed axes by 3 Euler angles? I see this statement in ...
2
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1answer
37 views

Lagrangian of a block connected to a circular track [closed]

Could someone help me? I am having trouble with obtaining the same result in part b) for this problem: Using the Lagrange Equation with respect to $\theta$, I obtained ...
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2answers
427 views

Classical Rutherford scattering (partial) derivation

I am having trouble answering the following question, please could you help! Thank you in advance for any assistance you can give. Consider classical Rutherford scattering of a particle with mass $m$ ...
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1answer
30 views

Determining Height of Platform on Fulcrum

Consider this scenario: We have a platform resting on a fulcrum. The platform's tilt is controlled by a motor attached to 2 levers: Is the link between the height of the top of the lever ...
3
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1answer
58 views

Application of Euler-Lagrange equations (Trivial problem, instructive one)

I have some doubt about a really trivial and simple problem in which I have to use ELE. Supposing I have a pendulum, in which the rope is a spring, so it's length may change in time. I have a mass ...
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0answers
24 views

Pivot Point Equations [closed]

Assume we have a platform fixed to a pivot point: -Forgive the crude image- We use 2 rods, either side of the pivot point, but at different distances from it. If we were to lift ROD 1 by a certain ...
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0answers
46 views

Acceleration in a space capsule which is falling to the earth [closed]

At first I apologize for asking such a career killing question in such an elite platform. Today I tried to prove something to four graduated engineers which I will mention below. The argument ...
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1answer
30 views

Expressing angular velocity of solid body [closed]

The problem: We have a circular disk of radius $R$ and mass $M$ that is mounted on a rotation axis that is not the axis of symmetry of the disk. The moment of inertia with respect to the axis of ...
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0answers
21 views

Does nature prefer second order differential equations? [duplicate]

We all know Newton's second law: $m \ddot{x} = F(x)$ or equivalently Euler-Lagrange or Hamilton's equations. In quantum mechanics the Schrödinger equation is also a second order differential equation. ...
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20 views

should transverse and longitudinal phonon velocities be equal for this mass spring system?

Let's say we have a cubic lattice of identical masses $m$, each connected to its 6 nearest neighbors by identical spring constants $k$. Essentially, the problem is I get an eigenvalue problem with ...
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1answer
28 views

An electron moving in a vacuumed chamber

Consider an object of mass $m$, e.g. an electron, moving in a straight line with constant non-relativistic velocity $\vec{v}$ in a vacuumed chamber, such that there are no collisions. Imagine the ...
3
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2answers
97 views

How mass is determined in dynamics?

Mass is one of the most core and complicated concepts in dynamics. I have tried many books but I still don't have a good idea of how the mass of any object is determined relative to another. In The ...
3
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1answer
327 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: The definition of rigid body is $$\left\lvert \vec{r_i}-\vec{r_j} ...
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6answers
2k views

Degree of freedom paradox for a rigid body

Suppose we consider a rigid body, which has $N$ particles. Then the number of degrees of freedom is $3N - (\mbox{# of constraints})$. As the distance between any two points in a rigid body is fixed, ...
3
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2answers
100 views

If gravity dropped off with the cube of distance

If gravity, for instance, dropped off with the cube instead of the square of distance from the Sun, would the planets still follow elliptical paths?
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1answer
88 views

Why does the pen does not move straight?

If i put a pen on a table in its horizontal position and then i try to move it horizontally by giving it a small push, so that it would fall off a table, i expect it to move horizontally but my pen ( ...
3
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1answer
97 views

Rigorous definition of degrees of freedom

According to this Wikipedia article, the definition of degrees of freedom is: The degree of freedom (DOF) of a mechanical system is the number of independent parameters that define its ...
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0answers
26 views

Stewart platform formulas [closed]

What kind of formulas/equations are commonly used to implement Stewart Platforms in electronics and mechanics? Using a co-ordinate system, how would you determine the position of each actuator, etc?
2
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1answer
46 views

Changing the length of a spring [closed]

Imagine we have a spring that is hanging from the roof with $k = 200$ and a stone with $ W=10N $ is pulling it down. Then due to $$ F=kx $$ we have $x=.05m=5cm$ Now we halve the length of the spring. ...
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1answer
36 views

Composite bar in series paradox

2]2 Here is the progress and the problem that I encounter. I can calculate the tensile force but it seems like the force cannot exist in the first place ? P/s: I am sorry because I can only pose the ...
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0answers
11 views

compound bars in series

Compound bars 1 and 2 have lengths L1 and L2, areas A1 and A2, Young moduli E1, E2,thermal expansion coefficient a1 and a2. subjected to a change of temperature T. Two ends of the bar are fixed. The ...
0
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1answer
29 views

Falling objects with different masses

I know that free falling objects with different masses fall at the same rate but that does not explain why objects with big masses are heavier to lift? what is gravity anyway I know it isn't a force ...
3
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3answers
124 views

How can I model the acceleration/velocity of a bicycle knowing only the power output from the drivetrain and rider weight?

I am currently building a simplistic video game of bicycle racing, a similar to the idea of Zwift. In this game, the user has a physical bicycle that is connected with various hardware that will let ...
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0answers
26 views

Two compound bars connected in series hanging vertically [closed]

I have a steel and a copper connected in series. We know the original length, cross area and young modulus of both bars. Now we hang it vertically, connected the upper end of copper to the ceiling and ...
0
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1answer
64 views

How to calculate the thrust of a rocket with relativistic exhaust

The general thrust equation is $F = \frac{dm}{dt}\cdot v$, where $m$ is propellant's mass and $v$ is the exhaust velocity, is the equation right? What if the propellant is highly relativistic? One ...
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1answer
125 views

We cannot solve this inclined plane problem, right?

We drag a sledge along a snow-covered hillside with constant speed. Distance is 150m. The time it takes to reach the top is 300 secs. The sledge is 12kg. And the coefficient of friction $\mu$ = 0.04. ...