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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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
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 ...
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
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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0answers
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 ...
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2answers
98 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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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
votes
1answer
100 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?
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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 ...
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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 ...
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
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 ...
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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 ...
3
votes
2answers
98 views

Principle of least action: $\frac{d S_{cl}}{dt_b} = \frac{\partial S_{cl}}{\partial t_b} + \frac{\partial S_{cl}}{\partial x_b}\dot{x}_b$

Question I cannot see how I can obtain the yellow highlighted section on the RHS from that of the LHS. The following equation can be found in both my lecture notes(*1) (page 9, equation 2.7) and is ...
0
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1answer
46 views

Calculate the change in mechanical energy for a system in presence of friction [closed]

The two masses in the figure are released from rest. after the $3$ kg mass has fallen $1.5$ m, it's moving with speed of $3.8$ m/sec. what is the change in mechanical energy done on the system during ...
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2answers
74 views

Is rotational motion of the centre of mass impossible?

We know that for a system, the center of mass $CM$ moves as a particle as though all the forces on the system were acting on it. So does that mean rotational motion of the center of gravity ...
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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1answer
48 views

Moment of inertia of orbiting sphere

Is the moment of inertia of a sphere orbiting some object equal to the moment of inertia of a point mass at the same distance away from the object?
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1answer
53 views

How am I able to keep my footing on an accelerating platform?

When I'm standing in a train car and the train starts slowing down relatively quickly, I instinctively flex certain muscles in my legs and that helps me keep my footing. What muscles am I flexing ...
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1answer
47 views

Does more surface area mean more traction?

I came across this question when considering new vehicle tires in a snowy environment. It appears that big off-road tires have very deep treads which greatly increase the surface area of the tire. ...
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2answers
65 views

Are the generalized coordinates in Lagrangian mechanics really independent?

In Goldstein's Classical Mechanics, Chapter 2.3: Derivation of Lagrange's Equations From Hamilton's Principle part of the derivation involves each of the generalized coordinates being independent. $$ ...
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0answers
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Rotation, translation or both. [closed]

the square is the same material throughout, equal mass distribution. In this case, will the object rotate, translate or both and why ? Thank you.
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1answer
39 views

Force (torque) to break a bike handlebar? [closed]

Few weeks ago a neighbor manage to hit my bike with his car while the bike was parked next to a wall, check the picture. One side of the handlebar was at the wall and the door of his truck hit ...
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0answers
57 views

Cauchy stress tensor for a spherically symmetric problem [closed]

Given a sperically symmetric problem, I am asked to show that its Cauchy stress tensor, in spherical coordinates will assume the form: ...
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0answers
58 views

An intuitive explanation of the so called Galileoʼs theorem

The statement of the theorem is as follows (see Francisquini et al, Physics Education, Volume 48, Number 6, November 2013): Prove that the time taken for a particle to slide from the highest point, ...
3
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1answer
169 views

How to show period is defined by $T=dS/dE$ (V.I. Arnold Mathemtical Physics)

I'm looking at a book by VI Arnold on mathematical physics and I've hit a roadblock pretty early on. I'll quote the question: "Let $S(E)$ be the area enclosed by the closed phase curve ...
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1answer
77 views

Derivation Of Euler-Lagrange Equation [closed]

I want the proof of this relation in details, $$ \frac{\rm d}{{\rm d}t}\left(\frac{\partial\vec{r}_v}{\partial q_\alpha}\right)=\frac{\partial\vec{\dot{r}_v}}{\partial q_\alpha} $$
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0answers
47 views

Internal energy in classical and quantum mechanics [closed]

What is the difference between classical and quantum mechanics of rotational, translational and vibrational energies?
0
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1answer
66 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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2answers
50 views

Conservation of angular momentum in a collision

Suppose I have a stick hinged to a pivot and it is released from its horizontal position and just after it becomes completely vertical, it strikes a ball completely stationary as in the given figure ...
3
votes
1answer
108 views

Why isn't kinetic energy conserved in this rotational dynamics problem?

Consider a uniform rod which is spinning about an axis that goes through its centre, perpendicular to the rod itself. Two small rings are attached on the rod at equal distances from the centre. As the ...
0
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3answers
76 views

Why can't we define a potential energy for a non-conservative force? [closed]

We could define potential energies for non-conservative forces too and then we could conserve it with kinetic and potential energy as we know it. But no one does that. Why is this? Please explain. Any ...
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0answers
28 views

The force of a spring

I am new in continuum mechanics and I want to prove the formula which gives the force given by a spring : $$F_{max}= \frac{Ed^4(L-nd)}{16(1+\nu)(D-d)^3 n}$$ where : $E$ – Young's modulus $d$ – ...
0
votes
1answer
108 views

Can Newton's 3rd Law be considered as a direct consequence of the coulomb's law of electric interactions? [closed]

Let me explain my thought. Lets consider Coulomb's definition of electric force between two charges as the fundamental law. Under this consideration, forces between charges already follow What ...
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1answer
238 views

Flipping a deck of cards: why do the cards cluster?

First let me describe what I mean by flipping a deck of cards. Fan a deck out, take the card on one side, flip it - then, much like a string of dominos, the rest of the cards are flipped and end up ...
0
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1answer
47 views

Spring Potential Energy [closed]

A spring whose spring constant is $k$, having an initial "free" length is $l$, is being pressed by $2$ hoops on a metal(the parabola) on his both sides. (see image below) I want to calculate the ...
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0answers
31 views

The change in time of a concentration in a fluid can be described by Reynolds' theorem. Is that the whole story?

Let $d\in\left\{2,3\right\}$ and $\Omega_t\subseteq\mathbb R^d$ be the bounded set occupied by a fluid at time $t\ge 0$. Moreover, let $\eta_t:\Omega_t\to[0,\infty)$ be the concentration of imaginary ...
0
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2answers
40 views

In a vacuum, given two identical objects, if one is stationary, what would happen if the two objects collide?

Given these two identical objects, if one is stationary, and the centre of mass of the other object collides head on with the centre of mass of the object that is stationary, i.e it does not come into ...
0
votes
1answer
49 views

How are unbalanced forces even possible, given Newton's 3rd law? [duplicate]

The notion of an unbalanced force seems to contradict Newton's third law, entirely. For instance, apparently, if you push a rock, then an unequal force is being applied in the opposite direction with ...
1
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0answers
26 views

Height of water in vessel containing gas [closed]

The question reads- Thin walled Cylinder of height h, mass m and cross section A filled with gas and floats on water. Now due to leakage depth of submergence increases by $\Delta h$. $P_o$ is the ...
1
vote
1answer
63 views

How is it possible to vary time without affect the coordinates or their derivatives?

In the context of Noether's theorem , the Hamiltonian is the constant of motion associated with the time-translational invariance of the Lagrangian. Time-translational invariance is equivalent to the ...
2
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1answer
40 views

Why is the potential independent of the generalized velocity?

In Goldstein, Classical Mechanics, Chap. 1.4 we derive Lagrange's equations from D'Alembert's Principle. My question is regarding the last part of the derivation, specifically the part where he ...
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0answers
102 views

Classical proof of the gyromagnetic ratio $g=2$

I was reading Representing Electrons: A Biographical Approach to Theoretical Entities, by Theodore Arabatzis. At a certain point, where he is explaining the history of the magnetic moment of the ...
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0answers
35 views

What is the probabililty that a fair coin lands on its side?

This is a popular gag in movies, but I wonder how likely it really is. What is the probability that a uniform cylindrical coin (with radius $1$ and height $h$) lands on its side? If the ground were ...
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0answers
20 views

Finding maximal angle after elastic collision [closed]

Let $m_1=400gr, m_2=600gr$ represent the masses of two balls. the two balls are hanging from the ceiling ($m_1$ is right to $m_2$), and then someone pull to the right side the $m_1$ ball in an angle ...