# Tag Info

### Is this proof that massless objects cannot be charged?

As described in Michael Seifert's answer, the question requires relativity, not Newtonian mechanics. As explained in the comments by Andrew Steane and Michael Seifert, the question also requires ...

### Is this proof that massless objects cannot be charged?

The correct answer is your parenthetical possibility that "Newton's laws don't work for massless objects in nonrelativistic physics." This has nothing to do with electricity or electric ...
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### Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

Mass is seen as a scalar. In differential geometry, it's volume or density forms that are integrated. So even mass would be seen to have a directional character given by the density form. Nevertheless,...
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### Estimate the revolutions per minute for which the engine will experience the greatest vertical vibrations

If the object sinks to $x_0$ you want to use the equilibrium condition $k x_0=mg$ to estimate the natural frequency of the motor-rubber floor system. This then becomes the resonant angular frequency ...
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### Is this proof that massless objects cannot be charged?

As was pointed out in the comments above, one has to use relativistic mechanics to talk meaningfully about massless particles; you can't just write $F = ma$ and expect it to work. And, indeed, it ...
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### Is this proof that massless objects cannot be charged?

I disagree with your conclusion that $qE=0$ if $m=0$. My interpretation is that in such a case the acceleration is infinite, so the product is well defined. It is only natural to think that in ...
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### Is this proof that massless objects cannot be charged?

I think a massless electron traveling at $c$ under classical Maxwell's Eq. would be problematic, but: The Standard Model says electrons were massless and charged before Spontaneous Symmetry Breaking, ...
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### Can something have momentum but not velocity?

The idea of momentum is fundamental, even more fundamental than velocity or mass. This is not correct. At best it is a matter of opinion what is "more fundamental." In the classical ...
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### Can something have momentum but not velocity?

thinking about photon, it has constant speed, so when a force, like gravity is applied to it, because there is no mass, It changes the direction of the photon, and also the frequency. having an object ...
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### Torque in torsional pendulum

So there's a lot of information about a torsion pendulum system been abstracted away given the basic $\tau = -c\theta$ equation. Essentially, the string in a torsion pendulum has a non-zero thickness, ...

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### 2DOF robot arm dynamic model (Double Compound Pendulum - Modeling without Lagrangian)

I think I have found the problem and a solution. The problem is: We cannot model torque produced by the motor as a single force vector at distance r. It is rather distributed over the circumference of ...
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### Minimum energy required to behave like a turning point?

The basic problem you are running into is that different inertial observers do not agree on kinetic energy of objects or systems, but they do agree on changes in the system's kinetic energy. But on ...
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### What are the implications on the mechanics of connected particles over a pulley if the connecting string is not considered to be light?

To see this we don't really need the pulley, and the pulley just makes things more complicated. So let's think about the simplest case we can: Two blocks connected by a ("heavy") string, ...
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### What are the implications on the mechanics of connected particles over a pulley if the connecting string is not considered to be light?

A hanging string must supply tension to support whatever is below it. For a massless string, this is just whatever mass is attached to the end of the string. When the string has mass, we also must ...
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### Minimum energy required to behave like a turning point?

The issue is not in considering the potential in a different reference frame, the issue is in defining what the "turning point" means in different reference frames. I will use the example (...
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### Including air resistance, what is the escape velocity from Earth?

Assume the initial velocity is v, assume a function exists v(t) that tells the velocity at time t. The derivative of this function is acceleration. Air resistance is 1/2pv(t)^2CdA (where Cd and A is ...

### What's the relationship between the positions of each mass in this concentric pulley?

Assuming x1, x2 are positive lengths we can write x1/R1 = x2/R2
1 vote

### Modelling friction as a conservative force

For systems with a Hamiltonian formulation, the Poincaré recurrence theorem (PRT) would indicate that most trajectories will eventually evolve back to a state arbitrarily close to their initial ...
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### Modelling friction as a conservative force

It's not possible to do what you are attempting. For friction to be a conservative force, then the net work done by moving along a path where the start and endpoints are the same is zero which would ...
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### Modelling friction as a conservative force

Adding friction to a Lagrangian is not commonly taught. It is non-trivial, but not too difficult in the end. The key element is producing a "dissipation function" $D$ that we can use to ...
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### Why is Hamilton's equations sometimes written with a gradient?

The simplest answer is, that it's a far more compact/applicable form of notation generalization, especially when dealing with various types of field theories (both classical or quantum). In general, ...
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### Why is Hamilton's equations sometimes written with a gradient?

Your best guess is correct. Let's take the example of an $N$ particle system in $\text{3D}$. If I wanted to define my generalized coordinates as just the position of each particle, then one way I ...
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### Problem 6.3 from David Morin (classical mechanics)

Note that the Euler-Lagrange's equations for a set of $\{q_1,\dots, q_n\}$ generalized coordinates are valid if the $n$ coordinates are independent from each other. The $x$ coordinate of your problem ...
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### Why the amplitude of monopole solution in Helmholtz equation is complex?

If there is a single monopole it does not matter whether $A$ is real or not but if you have two or more sources then their relative phases, and thus the phase of $A$, do matter. The same holds if the ...
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### Calculating the total time of the movement in horizontal movement

Assuming that there are no dissipative forces and that the ball was initially at rest($v_0 = 0 \frac{m}{s}$). The ball then takes time $t_0$ to cover a distance of $\Delta x_0 =15m$. This time may be ...
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### Can the value of friction force ever exceed value of applied force?

First, there is an important qualification to "the value of friction force can never be greater than the applied force". This refers to static friction. Indeed, you pose a scenario where &...
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### Integration by Parts in Liouville's Theorem

The first thing to note, which I leave to you to verify, is that $D_H$ is a derivation on smooth functions, meaning it is linear and satisfies a product rule: \begin{align} D_H(FG)=(D_HF)\cdot G+F\...
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### Can the value of friction force ever exceed value of applied force?

To answer the question in the title, the friction force can be larger than the normal force that is producing it. There is no restriction. Coefficients of friction larger than 1 are not common in ...
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### Can the value of friction force ever exceed value of applied force?

No. You've discovered the Class 2 Lever, which places the load between the input force and the fulcrum. You have correctly calculated that the friction force is 4 times the input force. The reason for ...
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### The Hamiltonian of a system under only the effect of an electric field

This answer is meant to address your comment to Roger Vadim's answer (which is clear and correct). Newton's 2nd law for a charge in a uniform electric field says that \begin{align} q \mathbf{E} = m \...
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### The Hamiltonian of a system under only the effect of an electric field

The question is unrelated to quantum mechanics, and even to classical mechanics (dealing with Lagrangians and Hamiltonians), but rather to the basic Newtonian mechanics: Indeed, when a particle is ...
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1 vote

### What quantity can a microstate have?

A microstate is defined as a specific microscopic configuration that a system can have. One of the primary goals of statistical physics is to see the relation between microscopic proprieties and ...
1 vote

### In an $n$ particle system, why is the Hamiltonian summed over $n$?

The index $i=1,\ldots n$ is a particle index; not a coordinate index. The $i$th particle carries a 3-momentum $p_i\in\mathbb{R}^3$. In the Hamiltonian $p_i^2=p_i\cdot p_i$ is a dot/scalar product. ...
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The hamiltonian is a scalar quantity as it represents total energy of a system. Each particle momenta in your equation $(1)$ is the magnitude of said particle's momenta $p_i = \sqrt{\sum\limits_i^d \... • 165 2 votes ### Proper conceptualization & notation for vectors,$n$-tuples, and matrices in physical space We should distinguish between vector spaces and the manifolds upon which they are tangent. A vector space is an abstract space where addition between the elements of the vector space is defined, as ... • 674 9 votes ### Proper conceptualization & notation for vectors,$n$-tuples, and matrices in physical space I think the core of your question is a very commonly-misunderstood subtlety, so I'll begin with a seemingly abstract example. Consider the vector space$V$which consists of formal polynomials of ... • 51.8k 1 vote ### Can we deduce the conservation of mass in non-relativist physics or is it just an experimental fact? Fundamentally, we don't deduce things in physics. We experiment and observe, and adjust our mathematical models accordingly. All deduction from math is suspect when applied to physics. Mathematical ... • 4,113 1 vote Accepted ### Lagrangian Mechanics - Is the Given Answer Incorrect?$\dot{\phi}$is not a constant of the motion, so you can't treat it as constant when taking the derivative of$V_\text{eff}$with respect to$\theta$. If you leave$V_\text{eff}\$ in its original form,...
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