Questions tagged [classical-mechanics]

Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].

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Acceleration-Meter

I encountered a Physics Olympiad problem: A ball bearing rests on a ramp fixed to the top of a car which is accelerating horizontally. The position of the ball bearing relative to the ramp is used as ...
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0answers
30 views

What is the equation of motion of this question? [closed]

Determine the expressions for the kinetic and potential energies of this system using the counterclockwise rotation of each bar as the degrees of freedom. Do not assume small rotational angles and ...
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1answer
23 views

How to check the direction of friction in case of pure rolling

I was stuck in a question as follows: Here, I'm not able to understand that how to decide the direction of friction and about which point we should check the torque for the same purpose. Would ...
4
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3answers
150 views

In a general physical sense, the position of a particle is really a vector?

It's consistent define position of a particle in some frame as a vector or is just a Physics informality? Velocity and Acceleration can be added up and bring multiplied by real numbers an have ...
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21 views

Required power for a car

How much power is needed to accelerate a car from v0 to v1 in “t” seconds, given that it maintains a constant accerlation and air resistance and roll friction is not negligible? I’m not quite sure ...
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0answers
17 views

How to calculate the velocity and angular speed of a disk pulled by a rope? [closed]

I've seen a lot of questions about this situation but I can't find an answer. So you have a disk (radius: R = 100cm and mass: M =...
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33 views

Difference between finite and infinitesimal motion

I am studying Arnold Sommerfeld mechanics. Here they talk about finite and infinitesimal motion. Quoted from the text: The simplest example of a non-holonomic condition is furnished by a sharp ...
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0answers
26 views

Center of mass when surface mass density varies in 2 parameters [closed]

I found a question in my homework to solve which you have to find the center of mass of a semicircular disc. Specifics of the question in image However here the problem is that the density varies both ...
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0answers
17 views

Find partition function for a classical harmonic oscillator with time harmonic forcing

I have been trying to find partition function for classical harmonic oscillator with time harmonic forcing term and reached an expression. I want to know if I am correct. There is abundant ...
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41 views

A string struck by a hammer [closed]

I am having some trouble with my homework and there is just something I don't understand. The problem is a hammer striking a string with length $L$ vertically at speed $v$ on the location $a$, then ...
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1answer
32 views

A formula which relate spring constant to its physical properties like length and area of cross section

I know spring is a mechanical analogue of capacitor. And length of a spring is equivalent to plate seperation of capacitor. So what is the mechanical equivalent of area of cross section of capacitor ...
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2answers
66 views

What happens to the center of mass of a ice cube left on a table?

Let us assume we have a big ice cube on a rigid table(on Earth). After a while the ice cube will melt, if we are on Earth then the ice will get converted into water and spread on the table. ...
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2answers
51 views

When we push on a wall, can we say work is being done on the atomic particles in contact with our hand?

Since textbooks say work is act transfer of energy, it led me to think of the following assumption: Work is being done on the the atoms in the wall, in contact with the hands, when we push (hard) ...
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4answers
49 views

How to know charge of a particle from position and momentum?

It was mentioned in one documentary that the only think we need to know about a particle is it's position and momentum, so we can calculate every other quantity from this. If it is correct how do we ...
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2answers
271 views

Issues with Newton's third law and Euler's laws of motion

Consider a system of particles (index $i$). Let the force acting on each particle be $\mathbf{F}_i = \mathbf{F}_i^{e}+\sum_{j, j \neq i}\mathbf{f}_{ji}$, where $\mathbf{F}_i^{e}$ denotes the external ...
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41 views

Degenerate perturbation theory in classical mechanics

I would like to know if there is a way to properly do time-independent degenerate perturbation theory in classical mechanics. Any answer or pointer to a good source would be appreciated. The issue of ...
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4answers
175 views

Problem with Noether Theorem to prove that energy is conserved

Suppose an action $S = \int _{t_1}^{t_2} L(q(t),\dot{q}(t))$ that is invariant under an infinitesimal constant time translation $t \longrightarrow t' = t + \epsilon$, of course with $\epsilon = ...
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18 views

Hammer Throw optimal angle

The athlete in Olympic Hammer throw (track and fields) spins a heavy ball attached to a wire around to give it speed, and then throw it away as far as possible. The theoretical optimal throwing angle ...
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0answers
30 views

Could pressure washers solve the Australia bushfires problem? [closed]

The JetLev water pack puts out about 60 psi but can lift a 400 pound weight 30 feet in the air. A lot of water can be provided by just those water jet pack units, 1,000 gallons per minute, providing ...
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0answers
69 views

Why I find two possible $S$ of a free particle by solving the Hamilton-Jacobi Equation?

For a free particle, the Hamiltonian is $$H(p)=\frac{p^2}{2m}.$$ The corresponding H-J equation thus can be written as $$\frac{1}{2m} \left(\frac{\partial S(q,t)}{\partial q}\right)^2=- \frac{\...
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0answers
18 views

Calculating the velocity of a moving object based on reflection of a pulse [closed]

An astronomer sends a pulse of radio waves at an unknown object. The radio waves are sent at t=0, the reflection returns after 8 seconds. At t = 845.54 seconds the astronomer sends a 2nd set of radio ...
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19 views

Can constraint forces be parallel to virtual displacements?

It is often stated that virtual displacements must always be orthogonal to constraint forces. However, an example where this seems to fall apart is that of the Atwood machine, where the virtual ...
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1answer
65 views

How to find the canonical transformation if given the new Hamiltonian we want?

If we know the new Hamiltonian $H^{\prime}$ we want, and $H^{\prime} \neq 0$, how can we find the canonical transformations? For example, we want to transform the $$H(p,q)=\frac{p^2}{2m}+\frac{1}{2}...
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3answers
45 views

Kinetic Energy and Braking Distance [duplicate]

A car traveling at 50km/h will move 44 extra meters from the moment its brakes are applied fully. If the same car travels 100 km/h on the same road, how far will it move from the instant its brakes ...
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1answer
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An expanding, sliding charged tube's self-imposed electromagnetic induction

If I have a simple cylindrical electrically-insulating tube possessing a net electrostatic charge and allow the tube to slide parallel to the tube's axis, that tube will possess electric currents ...
4
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5answers
116 views

D'Alembert's principle and the work done by constraint forces in Atwood's machine

From what I understand, constraint forces do no work because they are perpendicular to the allowed virtual displacements of the system. However, if you consider an unbalanced Atwood machine, in which ...
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1answer
40 views

Understanding the relationship between $P=F/A$ in brain ventricles

Humans have a hollow space (see the colored part in the diagram below) inside our brain where cerebrospinal fluid is produced and circulated. A disease exists called "normal pressure hydrocephalus" ...
3
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1answer
61 views

Quantity conserved for the 3D spherically symmetric harmonic potential $V(r)=\alpha r^2$ [duplicate]

I know that in the case of the Kepler problem there is a quantity (other than energy, momentum,...) conserved which is the Runge-Lenz vector. Is there also an "exotic" quantity conserved for a 2-Body ...
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30 views

Perturbation theory classical and quantum physics

I have calculated the correction in frequency for harmonic oscillator potential with the perturbation $x^4$ both classical mechanically (Lindstedt-Poincaré technique)and quantum mechanically. And I ...
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1answer
55 views

Does the engine's thrust not contribute to the lift? [duplicate]

Does the engine's thrust not contribute to the lift? Here are my thoughts: There are two types of aircraft resistance, one is the resistance created to create lift, referred to as lift resistance, ...
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0answers
15 views

Can two classical objects be correlated and tested to produce the results of Malus Law?

Of course testing one pair is not enough and I’m talking about thousands of pairs, tested at multiple set points. To be specific the objects are 12 inch long throwing knives, one inch tall by 1/8” ...
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0answers
39 views

A reference for the book 'Physics for the Inquiring Mind: the methods, nature, and philosophy of physical science' [closed]

I'd like to ask whether the book Physics for the Inquiring Mind: the methods, nature, and philosophy of physical science by Eric M. Rogers is a good source for studying physics still nowadays. In ...
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46 views

Hamilton equations and phase space

Let $(M,\omega)$ with $M$ a $2n$-dimensional manifold and $\omega$ a $2$-form on $M$, furthermore let $(M,\omega)$ be a symplectic manifold (smooth, differentiable, continuous, whatever is needed for ...
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56 views

Quantum solitons: derivation of $ \int {\phi^\prime}^2 dx = M$ using Lorentz invariance

I was reading through page 10 of this document (Chua, 2017) on quantum solitons, and came across the following statement relating to the equation for kinetic energy $$T = \left(\frac{da}{dt}\right)^2\...
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0answers
20 views

Coupled position-momenta term in hamiltonian

I am studying a hamiltonian system of the form: $$H=H_0+b(x^ix_i)^{1/2}(p^ip_i)^{1/2}$$ In which $H_0$ is the hamiltonian of a completely integrable system and $b$ a real constant. I have tried ...
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2answers
49 views

Tire traction force, friction or reaction? [duplicate]

I'm confused with the nature of the force produced by tires that pushes the car forward. This is what I understand: Let us have a driving torque applied on the wheel axle clockwise. This will produce ...
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0answers
20 views

Friction and dragging a body up a ramp [closed]

A crate of weight 4000N is placed on a ramp inclined at 20 degree to the horizontal and is just on the point of slipping down the ramp. A workman then attaches a rope to the crate, to haul it straight ...
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0answers
43 views

Find initial velocity of ball using projectile motion and air drag included [duplicate]

Essentially, I want to create a general equation to find the initial velocity of the ball such that it hits a target (x, y). Include air drag. I understand completely how to find the initial velocity ...
0
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1answer
67 views

What is the velocity on perimeter of a wheel when it is hit by hand tangentially to increase speed?

This is a homework problem in Newtonian mechanics. The problem statement is A circular wheel (whose radius is $R$ and moment of inertia is $I$) is hit by a hand of mass $m$ repeatedly with a ...
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0answers
37 views

How to identify progressive waves by their equation [duplicate]

From my understaning, a simple progressive wave is written in the form: $y(x,t)=A \sin(kx \pm wt)$ (or its cossine equivalent) and it is a solution to the equation: $$\frac{\partial^2 y}{\partial x^2}=...
0
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1answer
29 views

Perfect gas relationship between pressure and density

I've been given the following equation for a perfect gas: \begin{equation} p = k \rho^\gamma \end{equation} Where $k$ and $\gamma$ are constants. I'm trying to find out where this comes from or a ...
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0answers
32 views

Tennis racket theorem [closed]

According to Tennis racket theorem, the rotation around the second principal axis become unstable. Then, what is the 1st, 2nd and 3rd principal axis of this object (video)?
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1answer
43 views

Why the action is taking phase in considering Huygens principle in matter waves?

From Dirac's remarks $$\langle x_2,t_2|x_1,t_1\rangle=\exp\left[ \frac{i\int_{t_1}^{t_2}\mathrm dt\, L_{\text{classical}}{\left(\dot{x},x\right)}}{\hbar}\right].$$ How can I conclude from Huygens ...
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1answer
25 views

Is the flow velocity above or below the inclined plane high? Why?

There is an inclined plane between the two plates. The fluid flows between the plates. Is the flow velocity above or below the inclined plane high? Why? As shown in the figure, the blue line segment ...
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0answers
63 views

Understanding the Staeckel conditions for separability of the Hamilton-Jacobi equation

I'm trying to understand the so-called Staeckel conditions, specifically the fifth one, for separability of the Hamilton-Jacobi equations, as described in Goldstein's Classical Mechanics (3:rd edition)...
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0answers
55 views

Vector field and phase space

Let's assume we have phase space of harmonic oscillator with vector field and coordinates $(x,p)$ like in this picture. Arrows represent the vector field. Let's take some coordinates $(x_i, p_i)$. ...
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2answers
21 views

Do curved moving objects tend to move away along the normal direction of the curve? [closed]

Do curved moving objects (Such as a ball moving along a curve path) tend to move away along the normal direction of the curve? Because of the centripetal force, it is not really far away, but every ...
2
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1answer
46 views

Can I determine a transformation matrix for a stress tensor with respect to the axes $O x_1 x_2 x_3$ to define new axes of maximum shear stresses?

Is it possible to determine a transformation matrix for a given stress tensor with respect to the axes $O x_1 x_2 x_3$ to define new axes $O x'_1 x'_2 x'_3$ of maximum shear stresses? To make my ...
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0answers
28 views

On ways of describing the shape of strings fixed at 2 points [duplicate]

I was trying to derive the function $h(x)$ that describes the shape of a string fixed at two points with distance $D$ (which aligned with the x-axis), in other words, $h(0)=h(D)=0$ but I got stuck. I ...
1
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1answer
38 views

How should it be approached the combined moment of inertia of a system and torque to find the angular acceleration of a system of pulleys? [closed]

I'm not very sure if the combined system of pulleys sharing a common radius should it be approached if it would be a single one. In either case, what would be the way to assess that situation?. To ...