New answers tagged

0 votes

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 ...
user avatar
2 votes

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 ...
user avatar
  • 41.5k
-2 votes

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,...
user avatar
-1 votes

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 ...
user avatar
  • 38.8k
15 votes
Accepted

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 ...
user avatar
3 votes

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 ...
user avatar
3 votes

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, ...
user avatar
  • 23.2k
0 votes

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 ...
user avatar
  • 7,589
-2 votes

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 ...
user avatar
  • 25
1 vote
Accepted

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, ...
user avatar
2 votes

Can something have momentum but not velocity?

Momentum does not require mass. For example the electromagnetic field carries momentum, the momentum density of the EM field is: $$\vec{p} = \epsilon_{0} \vec{E} × \vec{B}$$ For light: $$p = \frac{E}{...
user avatar
  • 4,366
0 votes

Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

The correct answer is "it depends". In calculus the area under a curve $y=f(x)$ is usually approximated using sections $\delta x$ that are the same size, and the limit is taken as the size ...
user avatar
  • 1,119
0 votes

Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

There are several possible answers to this question depending on the framework you use. The way you are thinking about "dm" suggests you are thinking about Riemann integral. In this integral,...
user avatar
  • 5,553
0 votes

Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

the answer to your question: not necessarily. depends upon your choice of variables you wish to evaluate dm with $$M= \int dm$$ $$M = \int \lambda dx$$ Let: $$x= t^2$$ $$dm = [\lambda 2t dt]$$ ...
user avatar
  • 4,366
2 votes

Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

The $ dm = \rho(x) dx $ expression tells us that $ m $ and $ x $ do not have generally equal binnings. When you integrate according to $ dm $, it is uniform w.r.t. mass, but not w.r.t. length, and ...
user avatar
  • 75
5 votes

Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

$\newcommand{\d}[1]{\mathrm{d}{#1}}$In general you can use a change of variables, to write $$\d{m} = \frac{\d{m}}{\d{x}}\d{x}=:\rho(x) \d{x},$$ where $\rho(x)$, defined as $\frac{\d{m}}{\d{x}}$, is ...
user avatar
1 vote
Accepted

Is every $dm$ piece unequal when using integration of a non-uniformly dense object?

I don't quite get the question, but yes, every piece of $dm$ has unequal mass, but equal length. And when you write $ dm = λdx $, the $λ$ you are writing is called the local linear mass density. In ...
user avatar
0 votes

How to find the direction of acceleration if an object is changing its direction of velocity but not magnitude then how we can find the direction

If velocity keeps the same magnitude at all times, then: $$\lVert\vec{v}\rVert=\text{cst} \quad\Rightarrow\quad \vec{v}.\vec{v}=\text{cst}$$ Derive this expression with respect to time: $$\vec{v}.\...
user avatar
  • 2,256
0 votes
Accepted

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 ...
user avatar
  • 111
1 vote
Accepted

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 ...
user avatar
  • 1,049
0 votes

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, ...
user avatar
  • 1,049
0 votes

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 ...
user avatar
0 votes

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 (...
user avatar
  • 65.8k
0 votes

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 ...
user avatar
0 votes

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
user avatar
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 ...
user avatar
0 votes

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 ...
user avatar
4 votes

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 ...
user avatar
  • 65.8k
1 vote

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, ...
user avatar
  • 184
3 votes
Accepted

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 ...
user avatar
0 votes

How to solve the Helmholtz equation in damped oscillator BCs?

Short answer: Replace $\omega$ with $\omega-i\xi$. Longer Answer: The Helmholtz equation is derived from the wave equation, which may be written as $$\nabla^2P -\frac{1}{c^2}\frac{\partial^2P}{\...
user avatar
  • 1,392
0 votes

When to apply $I_c \underline{\omega} = \underline{M_c}$?

Cylinder rolling in the inclined plane. starting with the free body diagram , you obtain two equations translation $$m\,\ddot s=-F\tag 1$$ rotation $$I_{\text{CM}}\,\ddot\varphi=F\,r+\tau\tag 2$$ now ...
user avatar
  • 8,555
2 votes

When to apply $I_c \underline{\omega} = \underline{M_c}$?

The expression $ \underline{M}_c = \mathrm{I}_c \,\underline{\omega}$ is never correct. I think you forgot the time derivative of rotational velocity here. Also, the are Coriolis torques that relate ...
user avatar
  • 33.5k
3 votes
Accepted

What do you think about this particularization of the Euler-Lagrange equation that resembles Newton's 2nd Law?

Yes, one may use d'Alembert principle to rewrite Newton's 2nd Law as Lagrange equations $$ \sum_{i=1}^N\underbrace{\left(\dot{\bf p}_i-{\bf F}_i\right)}_{\text{Newton's 2nd Law}}\cdot \delta {\bf r}_i ...
user avatar
  • 170k
2 votes
Accepted

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 ...
user avatar
2 votes
Accepted

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 ...
user avatar
  • 9,700
0 votes

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 ...
user avatar
  • 1
6 votes

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 &...
user avatar
  • 3,375
1 vote
Accepted

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\...
user avatar
  • 2,824
2 votes

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 ...
user avatar
  • 6,568
20 votes

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 ...
user avatar
  • 8,982
1 vote

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 \...
user avatar
  • 6,259
1 vote
Accepted

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 ...
user avatar
  • 39.1k
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 ...
user avatar
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. ...
user avatar
  • 170k
1 vote
Accepted

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

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 \...
user avatar
  • 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 ...
user avatar
  • 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 ...
user avatar
  • 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 ...
user avatar
  • 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,...
user avatar

Top 50 recent answers are included