In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.

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Impulse from absorbing a photon? Is there an increase in rest mass?

I'm going through A P French's special relativity. In one chapter (6) the following is set up: Suppose that a stationary particle of mass $M_0$ is struck by a photon of energy $Q$, which is ...
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4answers
262 views

Complex conjugate of momentum operator

Consider momentum operator representation in position space. $$\hat{p}=-i\frac{\partial}{\partial x} \,\ \text{and its eigen functions are } e^{ipx} \,\text{and} \,\ e^{-ipx}.$$ ...
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1answer
39 views

Work done or not in this case?

I have a very simple question. A motorboat directed upstream is seen to be at rest from the bank of a river. Is the engine doing any work? Is it right to say that since it is not causing any ...
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1answer
78 views

What happens to the acceleration of a body undergoing constant force?

Here's the problem I have, specifically relating to a rocket in deep space: A rocket burns fuel at a constant rate. Assuming its mass remains constant, what happens to its acceleration? I seem to get ...
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1answer
53 views

How we can manipulate the momentum of a particle?

Is there any way to affect a particle's momentum value?
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1answer
155 views

Interpretation of Conjugate Momentum in Field Theory

The conjugate momentum density, following as a conserved quantity with Noethers Theorem, from invariance under displacement of the field itself, i.e. $\Phi \rightarrow \Phi'=\Phi + \epsilon$, is given ...
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19 views

Definition of momentum-entangled particles

When we can say that two particle are momentum entangled ? I just read an article where it's said that two momentum entangled particles share the same momentum value in opposite directions no matter ...
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3answers
187 views

Why don't we substitute for $p$ in $E = pc$?

See, the energy of a photon is given out by $E = pc = hv$ why don't we substitute for $p$ in $E ^2= p^2 c^2 + m^2 c^4$ by putting $p = \gamma mv$ and then get a value for $m$ (which will be $0$ for a ...
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0answers
399 views

Nuclear reaction: creation of deuterium

A proton p collides with a neutron(at rest) n at relatively low-energies and creates a 'deuterium-core' d: $$p+n->d+\gamma$$ Find the wavelength for the photon as a function of the proton's ...
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64 views

Measurement of Mass and Momentum of a particle simultaneously

In quantum mechanics can the mass and the linear momentum of a particle be measured precisely or do they commute ?
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56 views

What are the general solutions to a hard sphere collision?

Surely someone has found the solutions to the hard sphere collisions (in $n$ dimensions) of two bodies of mass $m_1$ and $m_2$, respectively--that is the resultant velocities (or momenta) of the two ...
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0answers
401 views

kinetic energy in collisions [closed]

We were hoping you could help us understand collision energy. Vehicle $ A $ is driving West at $35\space mph$ and weighs $ 1437 \space kg$. Vehicle $ B $ is driving North at $35\space mph$ and weighs ...
2
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3answers
158 views

Equilibrium that is not stable

Consider a system which is in an equilibrium state. Now, a small perturbation causes it to start oscillating about the equilibrium state, but over time, the momentum with which it overshoots the ...
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1answer
58 views

Recoil from a shotgun

First of all I'd like to point out that I'm a complete layman when it comes to physics and I apologise if this isn't the correct forum for this. If I were to sit on an office chair on a laminated ...
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2answers
39 views

Calculating the Probability Current of a Travelling Wave

Calculate the probability current density vector $\vec{j}$ for the wave function : $$\psi = Ae^{-i(wt-kx)}.$$ From my very poor and beginner's understanding of probability density current it is : ...
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1answer
61 views

Colliding particles at speeds aproaching c [closed]

(In natural units where $\hbar=c=1$.) Two particles are to be collided. Each of these particles has a rest mass of 0.9 GeV and they will be collided at equal but opposite speeds. What is the minimum ...
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1answer
25 views

Do I need the exact velocity when experimenting with sliding coins?

I'm doing a home experiment but it's not going very well. I'm pushing coins on a table. I'm taking the time for how long it takes coin A to hit coin B and then I divide it by the time between them ...
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0answers
19 views

Calculating rate of change of momentum for a package [closed]

A helicopter is flying to the right (in the $+x$ direction) with a constant speed $v$, carrying a package of mass $M$ suspended below it using a cable as shown in the figure. (You can assume that $H$ ...
1
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3answers
206 views

Effect of incoming force on linear vs. angular velocity

First of all, I should note that I'm a programmer and have only an extremely basic understanding of physics; I only know how to explain my question in layman's terms and I apologize if I'm unclear or ...
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7answers
3k views

Does leaning (banking) help cause turning on a bicycle?

I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the ...
2
votes
1answer
90 views

In the Dirac equation, do $\alpha$ and $p$ commute?

The Dirac Hamiltonian is given as $H = \vec \alpha·\vec pc + \beta mc^2$ , Do the alpha and beta operators commute with the momentum operator? If yes then how?
6
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2answers
196 views

Why $-i\hbar\vec\nabla$ for momentum in quantum mechanics, while $m\vec{v}$ in classical mechanics?

I am a little bit confused when thinking of the momentum representation in QM and CM. In QM, momentum is represented as $-i\hbar\vec\nabla$, while in classical, momentum is represented as $m\vec{v}$. ...
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2answers
80 views

Momentum Operator in Quantum Mechanics

1) What is the difference between these two momentum operators: $\frac{\hbar}{i}\frac{\partial}{\partial x}$ and $-i\hbar\frac{\partial}{\partial x}$? How are these two operators the same? My ...
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1answer
132 views

Spring Damper System : Recoil Reduction

I am designing a man-"portable" 30mm sniper rifle. Although it may be classified as a anti-materiel cannon. I have the mass of the round in total, and the mass of the projectile leaving the barrel, ...
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2answers
76 views

Conservation of Mass, Momentum and Energy - Airburst Rounds

I have a airburst round with set amount of fragments with a certain shape inside my bullet. After a certain distance has travelled, a charge explodes in the back of the round disintegrating the shell ...
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0answers
53 views

Including special relativistic effects in momentum in Heisenberg's Uncertainty Principle

I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity. Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results ...
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1answer
77 views

Energy/Momentum required to deflect earth from its orbit

This question occurred to me when thinking about the firepower people have on earth. How hard is it to change the characteristics of the orbit of the earth when an explosion happens on its surface, ...
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2answers
352 views

Origin of motion and relative speed of bodies in the universe

Charged particles can hit the earth at relativistic speeds. But it seems that all large bodies have fairly low relative speed. Of course, speed can increase considerably when a body orbits close to a ...
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1answer
92 views

How do I calculate stopping power?

Malcolm Gladwell made a claim in a recent talk that a sling with a stone going at 30m/s has the same stopping power as a .45 calibre handgun. How would I verify whether or not this claim is true - ...
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2answers
83 views

Equal and opposite reaction - forces coming in pairs - or just common sense?

I've never understood why the conservation of momentum law is taught in schools as "every force has an equal opposite reaction". To me a gun's recoil is self explanatory; the explosion sits ...
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0answers
45 views

The question about MTW 4-momentum integral expression and lorentz nature

In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as $$ \tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu ...
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1answer
181 views

How do I show the fractional change in Kinetic Energy in a completely inelastic collision?

Given the formula $$\frac{{\Delta}(KE)}{KE_i}=\frac{(KE_f-KE_i)}{KE_i}=\frac{-M}{(m+M)}$$ Now I know these that the conservation of momentum is always applicable. Also I understand that ...
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1answer
51 views

The exact definition of conjugate momentum density

After checking various websites, I've seen the conjugate momentum density defined as either: \begin{align*} P_r ~=~ \frac{\partial \mathcal{L}}{\partial \dot{A}_r} \end{align*} or \begin{align*} P_r ...
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3answers
68 views

Confused about Impulse

Encountered a problem that involves impulse while studying for my exam and I'm not sure how to even approach it. I know that momentum is conserved, but I'm not sure how to relate that to avg force. ...
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2answers
54 views

Homework Question involving Momentum [closed]

I'm trying to solve a homework problem as review for an exam I have tomorrow and I was wondering if someone could help explain it to me. It is as follows: You are at Lowe’s shopping for bricks ...
3
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0answers
154 views

Practice AP Physics B Exam Question regarding Momentum

I am trying to review momentum for the AP exam coming up. I will be taking the AP Physics C exam for Mechanics, but I was just practicing on any free response questions I could find and I came across ...
2
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1answer
66 views

Relativistic fomulae for energy and momentum?

I know that the relativistic formulae for energy and momentum are: $E = \gamma mc^2$ and $\textbf{p} = \gamma m\textbf{v}$; Can we derive these formulae? If yes, where from?
0
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1answer
44 views

Help with momentum question involving vectors/trig [closed]

The problem: A car with a mass of 1200 kg and speed 10 m/s runs into a traffic barrier at an angle of 45 degrees, and is thrown outwards at an angle of 45 degrees relative to the barrier with a speed ...
5
votes
1answer
191 views

Why isn't $F = \frac{\partial \mathcal{L}}{\partial q}$?

If momentum is, $$p = \frac{\partial \mathcal{L}}{\partial \dot{q}}$$ and force is, $$ F = \frac{dp}{dt}$$ and by Euler-Langrange equations, $$ \frac{d}{dt}\frac{\partial \mathcal{L}}{\partial ...
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2answers
43 views

Final position of an object after aplying several horizontal forces [closed]

I'm given an object with a starting position. Several horizontal forces are applied to this object one after the other for different amounts of time. How can I determine the final position $x$?
0
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1answer
83 views

Classical disintegration of particles, Landau-Lifshitz series on Physics

i read Landau's book recently. In this book p.43 Landau says from (16.1) (16.2) can be write down $T_10$= $p_0^2$/2$m_1$=($M-m_1$)($E_i-E_1i-E_i'$)/$M$ For me, it is hard to understand the factor ...
0
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1answer
142 views

Why does a car bonnet (hood) rise when you connect the clutch with a brake on?

Is the rotational force to overcome the brakes moved to the opposite effect of moving the car chassis, until the brake is released?
2
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3answers
281 views

How does the solar sailing concept work?

Wikipedia describes solar sailing as a form of spacecraft propulsion using a combination of light and high speed ejected gasses from a star to push large ultra-thin mirrors to high speeds. I ...
2
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0answers
128 views

If photons don't have mass, how can they accelerate objects? [duplicate]

As far as I know photons don't have mass but they do have momentum ($p=mv$). Scientists say that if we put a shiny (reflective) shield of large radius in the vacuum of space, then light from sun will ...
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2answers
364 views

Impulse and Change In Momentum — Are they really different?

My entire time learning physics, I have simply assumed that Impulse and Change in momentum are the same thing. It makes sense -- Force changes momentum, and impulse finds the total of force. ...
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3answers
108 views

Movement in outer space via Newton's law of every action has an equal and opposite reaction

What is more effective for travel in outer space ignoring all other factors like air radiation etc. I have a 10 kg bag of rice would I travel faster throwing the whole bag at once or throwing a grain ...
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29 views

electron spin separation

I am having doubt whether the electron's up spin moment and down spin moment can be isolated from one another. If it got separated, will each moment acts as magnetic monopole (stable or unstable). ...
0
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1answer
93 views

Is there such a thing as instantly stopping?

I'm sorry if this is a stupid question, but I've never taken a physics class and I was curious about something. But anyway, my question is, is there such a thing as instantly stopping? For example, if ...
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2answers
115 views

A question about canonical momentum and arbitrariness for potential in magnetism

The following question confuses me: There exists magnetic field $B_z =- \beta x$ where $x > 0$, and a particle is incident from origin point $(0,0)$ with pisitive charge $q$, mass $m$, and ...
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0answers
75 views

Force needed to change momentum, from fixed position

I have a situation where I want to change the velocity of a mass, by applying a force from a fixed position. For example in the diagram below, the mass starts with the initial velocity in the upper ...