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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Dot Product Force

Konopinski's "What the electromagnetic vector potential describes" (Gaussian dimension) equation (3): $$\frac{d}{dt}[M\vec{v}+(q/c)\vec{A}]=-\nabla q[\phi-(\vec{v}/c)\cdot\vec{A}].\tag{3}$$ contains ...
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Why isn't momentum conserved in this pulley problem?

I have some conceptual doubt about method of solving this problem. 24. A block of mass $m$ and a pan of equal mass are connected by a string going over a smooth light pulley as shown in figure ...
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2answers
56 views

Doppler shift from a transversely moving plane mirror

Below is the diagram of the question I have on the Doppler shift of a light emitted from a stationary light source $S$ at an angle $\theta_1$ toward a transversely moving plane mirror $O$ having ...
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2answers
153 views

What canonical momenta are the “right” ones?

I'm doing some classical field theory exercises with the Lagrangian $$\mathscr{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu}$$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. To find the ...
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3answers
598 views

Why is momentum quantized in a 1D box even though the operator doesn't give eigenstates?

We don't get eigenstates of momentum when we operate momentum operator in the wave function of particle in a 1D box problem yet we say momentum is quantized in this situation. Why is it so?
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2answers
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Is it possible to jump by using only my arms?

We can see that basketball players use their arms to jump higher. Is it possible to lose contact with the ground by only moving my arms? I know that the calculations have something to do with ...
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2answers
189 views

How do waves have momentum?

A question on a practice test I'm taking is as follows: By shaking one end of a stretched string, a single pulse is generated. The traveling pulse carries: A. mass B. energy C. momentum D. ...
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211 views

Ball flying towards me - Newton's third law is violated?

I was trying to answer the question of the flying ball here on the basis of Newtons third law and Momentum conservation. Here is what I have tried. Lets take $m_1$ (the ball) hits $m_2$ (the man). ...
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2answers
134 views

In a CMCS 2-body system, why does the speed of the particles after collision stay the same?

A particle $m_1$ is traveling with velocity $v$ toward a stationary particle $m_2$. The velocity of the center of mass is given as $v_c=\frac{m_1}{m_1+m_2}v$. Changing to a moving coordinate system, ...
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93 views

difference between magnetic dipole moment and torque on a magnetic dipole?

I am a bit confused. What is the difference between magnetic dipole moment and torque on a magnetic dipole ?
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7answers
848 views

Why is momentum conserved (or rather what makes an object carry on moving infinitely)?

I know this is an incredibly simple question, but I am trying to find a very simple explanation to this other than the simple logic that energy is conserved when two items impact and bounce off each ...
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1answer
65 views

Fourier Transforms of position and momentum space in Quantum Mechanics

Fourier transformations: for momentum space and for position space. How do we know that Ψ is not the Fourier transform of Φ but we suppose that its the other way around(Ψ would be ...
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3answers
481 views

Conservation of momentum and energy in an explosion

One simple problem is physics is to determine the mechanical energy difference after an explosion. To do this, you must assume that momentum is conserved because in a explosion you have internal ...
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7answers
111 views

If we attach a fan at the end of a boat and switch it on, will the boat move? [duplicate]

I've been across a lot of questions like these, but I'm never quite able to get them. In this question, I reasoned that if I consider the boat and the fan to be a system, then there is actually no ...
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1answer
30 views

Terminal velocity of a raindrop

I have solved the question and got the answer , but I do not understand why will the raindrop attain a terminal velocity.Without any resistive forces why does it attain a terminal velocity?
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4answers
75 views

Is there difference in force when the height increases?

Consider a man with mass 50kg. When he jumps from a 2 meter height, the total force is $F=ma$ ie (mass * gravity), but nothing happens to him. When he jumps from a 50 meter height, the total force ...
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0answers
46 views

Conservation of Mometum in integral form

Water is pumped from one reservoir into a another. The pipe expands after a lenght of $L/2$ to a diameter of $d$. Given: $\dot{V}_p, \rho_w, d, \eta, L, p_p$ The previos tasks allowed ...
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1answer
42 views

4 momentum in particle physics, collision of positron and electron

If I have a positron striking an electron at rest to create 2 pions( + and -) and I want to calculate the minimum kinnetic energy that the electrons can possess to create these pions, then the created ...
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Can a Skydiver Land On a Large Slide and Survive?

Please forgive my lack of artistic ability, but here's my question: Consider that a skydiver, without using his parachute, were to fall exactly parallel to a giant curved slide that starts at ...
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3answers
289 views

Why Can a Skydiver Hit the Ground and Be Killed? [duplicate]

This is a follow on question from Physics SE Question "Can a Skydiver Land On a Large Slide and Survive?". User Steeven gives this answer here. User Dargscisyhp asks: What is it exactly that ...
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3answers
172 views

Why the nonexistence of a “one sentence layman phrase” for the de Broglie relation $p=\hbar k$? [closed]

(My question seems most likely will be considered a duplicate of OP (and possibly 1, 2, 3), but it turns out to be WAY TOO LONG as a comment in OP, and the system has deleted the corresponding chat ...
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3answers
120 views

What's faulty in my reasoning about energy and momentum in this problem?

The question (from Sparknotes SAT Physics): An athlete of mass 70.0 kg applies a force of 500 N to a 30.0 kg luge, which is initially at rest, over a period of 5.00 s before jumping onto the ...
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2answers
37 views

How is Linear Momentum different from Thrust?

I know both theories are different in a complex way, but how them differ from the first ideas of movement? I cant really tell the difference... Thanks!!
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1answer
140 views

Changing momentum of moving trolley

We have a trolley of mass $m$ and it is moving at a velocity $v$ along a smooth horizontal plane. It is full of water, and is leaking water at a constant rate out of the bottom of the trolley, i.e ...
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53 views

An Electron Chasing Another

An electron is held in place in deep space. Another electron approaches with speed $v_0$. When the approaching electron is a distance $r_0$ away from the first electron, the first is set free. The ...
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1answer
104 views

Is my proof of the thought experiment that Walter Lewin proposed in lecture 16 valid?

A tennis ball bounces off a wall elastically. The momentum of the wall changes, but the kinetic energy of the wall remains zero. How is that possible? Walter Lewin Lecture 16 - Ball bouncing on ...
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How did physicists arrive at conclusion that the product of mass and velocity is equal to momentum?

How did physicists arrive at conclusion that the product of mass and velocity is equal to momentum? What is the intuition behind $p=mv$? I had trouble finding any sources that state the actually ...
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3answers
58 views

Why can you turn on your bike without adding energy and still be moving?

There's a physical effect that I can't seem to figure out. When you are biking (on a bicycle), you have some speed. Then let's say you stop petaling and make a 90º turn to the right. You slow down, ...
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1answer
34 views

Rocket velocity during fuel burn [closed]

I know the formula for the velocity of a rocket after the on board fuel has been used up: $$ \Delta v = v_{ex} \ln\left( \frac{m_i}{m_e} \right) - gt $$ where: $v_{ex}$ is the exhaust velocity ...
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2answers
302 views

Symmetries of a Uniform Magnetic Field

Simple question. A system with a uniform electric field everywhere in space has translational invariance in the directions perpendicular to the electric field but no translational invariance parallel ...
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2answers
335 views

Does conservation of momentum mean a gyroscopic inertial thruster cannot work?

There is a device called the gyroscopic inertial thruster. Here is a Wikipedia article on it. I believe that this device cannot possibly work and that conservation of momentum proves that it cannot ...
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0answers
15 views

How to solve this energy problem using trends related to impulse and momentum? [closed]

The question runs a 1kg block moves with a speed of 10 m/s. It strikes a spring that has a spring constant of 25 N/m. Determine the maximum compression of spring. The energy way of solving ...
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1answer
15 views

How is the kinetic energy of an object in collision converted to work done in deforming itself?

Usually, in a perfectly inelastic collision, maximum amount of KE is lost. I guess it depends on the rigidity of that object collision if any KE at all will be converted to work done to deform. ...
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2answers
268 views

How does a rocket's exhaust gas' momentum propel a rocket?

During the launch of a rocket into space, the exhaust gases from the engine possess momentum. Outline, with the help of an equation, how this causes the rocket to be propelled upwards. Can ...
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4answers
8k views

Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
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1answer
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How is the final velocity in 2 body collision distributed between the 2 bodies?

Suppose 2 sphere of mass 1Kg move with velocity 5m/s and 10m/s in same direction. Let us call the ball moving with 5m/s blue and other one red with blue ahead of red from origin. Initial KE of Blue = ...
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1answer
168 views

Particle In a Box and momentum, velocity

So on a homework assignment, we are give the width of a well, $a$, and the mass of the particle $m$ and we want to find the average velocity of the particle at the n=1 state. So here is my attempt at ...
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10answers
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How to explain independence of momentum and energy conservation in elementary terms?

I'm trying to explain to someone learning elementary physics (16 year old) that linear momentum and energy are conserved independently. I'm not a professional physicist and haven't tried to explain ...
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5answers
398 views

In an elastic collision, can we choose between cons. of energy and cons. of momentum?

Suppose we have two solid spheres with masses $m$ and $M$, respectively, and that $m$ is significantly less than $M$. The lighter sphere is placed directly on top of the heavier one, and the two are ...
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2answers
76 views

Why are force, momentum, and kinetic energy derivatives of each other [closed]

Force $ma$ is the rate of change of momentum, or the derivative of momentum with respect to time $$\frac{d}{dt} mv = ma = F$$. Kinetic energy is the integral of momentum with respect to velocity: ...
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3answers
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In general, why do smaller guns have more felt recoil?

Why is recoil easier to control on a more massive gun compared to a smaller gun with the same bullet. Presumably the bullet leaves both guns with the same momentum, but the larger gun seems easier to ...
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4answers
196 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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1answer
44 views

When will a ball running between two downwards slopes stop going back and forth?

Two angles $a$ and $b$ meet at a point, making an angle $c$ between them. $a$ and $b$ are all $0 < \theta < π/2$. $c$ is $π/2 < \theta < π$ $a$ is to the left and opens to the left, $b$ ...
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2answers
108 views

Where does the equation $p=\frac{1}{c}\sqrt{T^2 +2mTc^2}$ come from?

Where does the relativistic formula $$p~=~\frac{1}{c}\sqrt{T^2 +2mTc^2}$$ come from? What is the derivation from Einstein's formula? $T$ is the kinetic energy $m$ is the mass $p$ is the momentum.
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249 views

Confused about elasticity and collisions

I was solving the following problem and the explanation to it confused me. There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and ...
69
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9answers
11k views

Can we theoretically balance a perfectly symmetrical pencil on its one-atom tip?

I was asked by an undergrad student about this question. I think if we were to take away air molecules around the pencil and cool it to absolute zero, that pencil would theoretically balance. Am I ...
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3answers
61 views

Does a gas in a container lose kinetic energy?

When a gas is in a container, it frequently collides with the container wall, exerting pressure. However, with a collision, kinetic energy ought to be transferred from the gas molecule to the ...
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3answers
62 views

Force to deflect ball colliding with wall

Suppose I have a ball with a certain coefficient of restitution. The wall can be considered indeformable and with infinite mass. Everything's in 3 dimensions, and the ball can hit the wall at any ...
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1answer
42 views

What does the second solution in an elastic collision represent?

A ball of mass 2 collides with a stationary ball of mass 1 elastically! In finding the velocities i end up with two solutions and am not sure how to understand the second solution Simplified ...
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2answers
80 views

Why does linear momentum change in this problem?

I found this problem in a Irodov's book. It's asked to find the momentum increment of the bullet-rod system. I wonder why the system momentum changes. They argue this: The bullet-rod system is ...