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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Collisions between an object and a wall

Is momentum conserved when an object bounces back against a wall? The wall doesn’t move, but the object moves in the opposite direction. Assume this is an ideal, elastic collision. If, initially, the ...
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50 views

$p^4$ in radial coordinates not Hermitian

Griffiths' quantum textbook claims in question 6.15 that "$p^2$ is Hermitian, but $p^4$ is not, for hydrogen states with $l=0$." First off, I am puzzled at his use of terminology. An operator is ...
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1answer
61 views

What is the function type of the generalized momentum?

Let $$L:{\mathbb R}^n\times {\mathbb R}^n\times {\mathbb R}\to {\mathbb R}$$ denote the Lagrangian (it should be differentiable) of a classical system with $n$ spatial coordinates. In the action ...
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146 views

Calculating $\langle x | \hat{x} | p \rangle$ in $p$ basis

I am trying to calculate $\langle x\ |\ \hat{x}\ |\ p\rangle$. I can work in the $x$-basis like so: $$\langle x\ |\ \hat{x}\ |\ p\rangle=\int dx'\langle x\ |\ \hat{x}\ |\ x'\rangle\langle x'\ |\ ...
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76 views

Why is momentum conserved in inelastic collisions? How is it related to momentum-impulse theory?

First of all I want to mention, that I've found many questions around this site and in other websites dealing with my question; however, I don't think they answer my question fully. So I am here to ...
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1answer
88 views

Elastic Collisions and Relative Velocities

In a 1D elastic collision, it is well-known that the relative velocities of the two objects (before and after the collision) are reversed. What is the extension of this result to 2D or higher? Is ...
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69 views

What is “momentum density” and why it important to QFT?

I am reading Quantum Field Theory for the Gifted Amateur. On page 98, they provide a summary of a basic canonical quantization procedure: Step I: Write down a classical Lagrangian density in ...
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138 views

Force of a Train

Imagine that there are two trains and the first train is twice as long as the second train. They have the same mass per unit length and they are traveling at exactly the same speed. If the first ...
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1answer
58 views

What matters more in the strength tester game at a carnival, momentum or force?

A buddy and I were arguing over which matters more in the strength tester game (assuming the same accuracy of the hit): 1) momentum or 2) force. He was arguing that if you swing the hammer directly ...
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2answers
93 views

Momentum conservation in an electromagnetic system?

Suppose that I have two charged particles in the configuration below. Let us assume the following: We apply a constant force $f$ to the the bottom particle so that it has a constant acceleration ...
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1answer
83 views

Redshift of a reflected photon from a solar sail

Can someone help me understand my mistake here? I'm thinking of a photon travelling with momentum $p=h/\lambda$ which reflects off a solar sail of mass $m$ travelling with momentum $p_0$ in the same ...
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1answer
107 views

What force counteracts friction when a block is pulled?

Firstly, I understand and apologize that this is more of a physics question than a math question. I noticed that when I pulled a book out from under a pack of gum, the gum stayed largely in place (it ...
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115 views

Why won't this reactionless drive idea work (motor with a moving weight in space)

I know people will say it violates many laws of motion and conservation but could anyone explain why it is so? It's NOT a question about free energy. Imagine a motor in space. It has an arm (rod) ...
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1answer
178 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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1answer
81 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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269 views

Explain Momentum

It's a shame for me to be in Year 12 and still haven't understood the concept of Momentum. This is what I think, and I know I'm wrong. But, it is a good place to start for you to explain: "Since the ...
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1answer
282 views

Deriving $p = mv$ from translational symmetry (momentum conservation law)?

"In classical mechanics, momentum is defined as the quantity which is conserved under global spatial translations or, alternatively, as the generator of spatial translations." (G.Parisi, ...
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1answer
128 views

Changing Momentum

Okay, so I am having a hard time wrapping my head around this. Before looking at the answer, I worked the example and got the answer only because I used dimensional analysis to get me to the right ...
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2answers
325 views

effect of vertical collision on kinetic friction and subsequent change in horizontal velocity

Suppose somehow a block of mass $m$ is moving on ground, and the coefficient of kinetic friction between the block and the block is $\mu_k$. If I drop a tennis ball(of same mass) on it from a ...
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4answers
501 views

Bat hitting a ball

When a bat hits a ball, consider two cases: 1) The batsman goes for a defense, and stonewalls it, to reduce its speed. 2) the batsman goes for a shot, e.g. a home-run, etc. in which case will the ...
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3answers
335 views

Displacement with zero velocity

I know that we can rotate a deformable object using internal forces only in space. Thus we can cause an angular displacement without the use of any external forces. The following youtube video shows ...
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1answer
161 views

Integration of constant: $\int dp = \Delta p$ in impulse formula

In University Physics, it has something like: $$\int \sum F dt = \int \frac{dp}{dt} dt = \int dp = \underbrace{p_2 - p_1}_{\Delta p?}$$ But I thought $\int dp = p$? Though my maths is really rusty ...
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157 views

Cyclic co-ordinates implying the constant velocity motion of center of mass of a system of particles

I'm reading the section on Central Force in my textbook (Goldstein's Classical Mechanics has a similar argument in the chapter titled "The Central Force Problem", first section), where we have the ...
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2answers
70 views

Can you launch an item farther by slamming into it or accelerating it along a length

I am trying to desgin a little penny balista toy (built with a 3d printer). The short description is that there is a track with a mass ("hammer") that slides along it. There is a stack of pennies in ...
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2k views

what is physical meaning of this partial derivative?

what is physical meaning of this partial derivative: $$\frac {\partial p_x}{\partial x}$$ i know how do i solve it when the case is just derivative but partial derivative is a bit Hectic!.
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115 views

Path integral in quantum mechanics

I am confused by the derivation in Srednicki QFT's chapter 6 from (6.8) to (6.9). In (6.8), we have $$<q'',t''|q',t'>~=~\int DqDp \exp[i\int_{t'}^{t''}dt(p\dot{q}-H(p,q))],\tag{6.8}$$ and ...
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4answers
131 views

What does “spread of momentum” actually mean?

I was reading Feynman's lecture in which Feynman invoked his own way of explaining the uncertainty principle using single-slit experiment. There I found: To get a rough idea of the spread of ...
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1answer
81 views

What is the relation between a basis transformation and an induced transformation $\psi(\Lambda^{-1} p)$ on the wave function? [closed]

I'm having trouble understanding why is $\psi(\Lambda^{-1}p')$ the correct wave function in the Lorentz transformed frame $p' = \Lambda p$. Suppose the state in frame $O$ is given by $$ ...
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1answer
73 views

newton's cradle with 2 balls dropped from same height at same time

I'm creating a logo and want it to be as exact as possible. The logo idea is a "Newtonian cradle", but with only 2 balls and on straight steel wire (can't be bend). What would happen if I dropped ...
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1answer
95 views

Conservation of relativistic momentum

I'm trying to prove that momentum, $\rho = m \, v \, \gamma(v)$, is conserved in all frames of reference. I'm having problems with the following situation that I made; momentum is not conserved to ...
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2answers
91 views

Dumbbell rotation

What if apply impulse to dumbbell consisting of two masses and massless rod? It is clear for me that left dumbbell will move straight line. But it is not clear for me what kind of motion will have ...
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1answer
71 views

What is the motion of a balloon with a person climbing on a ladder?

Suppose you had a balloon of mass $M$ in the atmosphere at rest relative to the ground, with a ladder attached reaching towards the ground. A person (of mass less than $M$) begins climbing up the ...
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401 views

Question of Conservation of Momentum

I think I understand the concept of conservation of momentum in an inelastic collision. However, what if two objects, one being more massive than the other, started out together and then separated ...
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57 views

Calculating speed of spheres in an asymmetric Newton's cradle?

If we assume there is an asymmetric Newton's cradle with 3 spheres of different masses and the first one is initialized with some certain speed can we calculate the outcome speed of the all the three ...
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2answers
75 views

How to show that $\partial S/\partial q=p$ without variation of $S$?

I'm trying to get some understanding in treating action $S$ as a function of coordinates. Landau and Lifshitz consider $\delta S$, getting $\delta S=p\delta q$, thus concluding that $$\frac{\partial ...
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1answer
108 views

What would happen if Newton's Cradle was made of other geometrical objects rather than spheres?

What would happen if Newton's Cradle was made of other geometrical objects rather than spheres? For example, what would happen if it was made of cubes and the contact area was larger?
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2answers
227 views

Case of the mysterious bullets (taken from Mad About Physics)

"Two ideal bullets, identical in shape, size and mass, strike the same target with the same speed just before the collision. Force meters at the target register two times the force value for bullet A ...
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4answers
190 views

Since everything with mass exerts a gravity force on everything else, why do objects float in outer space?

For example, if you were to go out into deep space, and just slow down and stop your rocket. Everything inside the rocket that's not strapped in, starts floating. Why is that if every object has mass ...
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3answers
107 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf ...
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1answer
62 views

$\dot \omega $ when momentum is conserved

If momentum is conserved when there is no externel force, why is there an acceleration when a momentum parameter is changed (inertia)? How does it accelerate with no external force? For example ...
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1answer
110 views

Simple expression for transitional pressure force

Consider a simple, circular orifice with an upstream, high gas pressure and downstream, normal atmospheric pressure. Consider also a flat circular plate that can be positioned anywhere along the ...
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2answers
141 views

Add weight in front or behind the moving wheel?

Consider a wheel with bearing and axle bar rolling on level ground. If I want to help the wheel continue moving longer(or faster speed), should I add weight by moving the rider body in front or ...
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1answer
179 views

Conservation of energy and momentum via the continuity equation in asymmetric time and space translation

I am confused about energy and momentum conservation, time and space translation symmetry, and the continuity equation. Suppose we have a mass $m$ in inertial space far from any gravitational ...
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1answer
146 views

What factors indicates inelastic collision?

I am watching this example from Wikipedia: I am wondering what factors would indicate that the collision of 2 objects will be inelastic (I know macroscopic scale impacts are never perfectly ...
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1answer
322 views

Inner product of position and momentum eigenkets

Let's define $\hat{q},\ \hat{p}$ the positon and momentum quantum operators, $\hat{a}$ the annihilation operator and $\hat{a}_1,\ \hat{a}_2$ with its real and imaginary part, such that $$ \hat{a} = ...
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1answer
77 views

Momentum of Light Question [duplicate]

Since light beams carry momentum, why would a person holding a flashlight not feel a recoil similar to that of a rifle being fired?
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1answer
265 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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1k 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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2answers
63 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 $x$?
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2answers
153 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 ...