Momentum Definition and 1000 Threads

We want to show that ##[\hat{ \vec H}, \hat{ \vec L}_T]=0##. I made a guess: we know that ##[\hat{ \vec H}, \hat{ \vec L}_T]=[\hat{ \vec H}, \hat{ \vec L}] + \frac 1 2 [\hat{ \vec H}, \vec \sigma]=0## must hold. I have already shown that $$[\hat{ \vec H}, -i \vec r \times \vec \nabla]= -...

I'm sure I've read somewhere that Jupiter has 99% of the solar system's angular momentum, which shouldn't be the case. However, I can't find a source for this, and any search online for the topic doesn't bring up any science sites. Did I mis-remember?

I am wondering why heavier bullets have a higher momentum than lighter bullets when using similar powder charges? At the muzzle, a typical 150 grain bullet fired from a 30-'06 will travel at around 3000 ft/s. A 200 grain bullet from the same rifle will travel around 2600 ft/s. (The velocities...

1. When an object attached to a fixed point with a string, is given a velocity and the string goes taut. So it says in this book (Applied Mathematics 1 by L. Bostock and S. Chandler) that when the string goes taut, the component of the velocity of the particle becomes zero in the direction...

I am confused with the following two questions: 1. A particle moves under the influence of a central force directed toward a fixed origin ##O##. Explain why the particle's angular momentum about ##O## is constant. 2. Consider a planet orbiting the fixed sun. Take the plane of the planet's...

A particle of mass m has kinetic energy E when it collides with a stationary particle of mass M. The two particles coalesce. Which of the following expressions gives the total kinetic energy transferred to other forms of energy in the collision? I keep getting C as my answer when the correct...

Hi All, I'm trying to get a better understanding of the momentum thrust given by an over-expanded rocket nozzle (I realize this case voids the isentropic flow assumption used for the 1D isentropic gas expansion equations typically used for rocket engine design since the normal shock is not an...

I think I get the approach. We first need to evaluate the term ##\dot A_{\mu} \nabla A^{\mu}## and then evaluate the 3D space integral; we may need to take the limit ##V \rightarrow \infty## (i.e ##\sum_{\vec k} (2 \pi)^3/V \rightarrow \int d^3 \vec k##) at some point. The mode expansions of...

Wikipedia says that they are the equivalents of momentum and force in rotational motion but I don't understand why this comparison is possible. The torque's dimension is N*m it seems like energy. What is this energy? Why angular momentum is not mass times angular velocity?

Say we have a motor attached to the Earth with gear A, that drives identically sized gear B. Gear B spins on its own axis and but is also attached to ground. Torque between gears is equal. Technically each gear has equal but opposite AM right, but If I take Earth into account, how is Ang...

I am trying to relate these equations to get the energy with respect to momentum based on particle wavelengths. I did the following: $$\lambda = h/p$$ so $$p= h/ \lambda $$ Then $$p=mv$$ and $$E=1/2mv^2$$ So $$E = pv/2 $$ But the answer was: $$E = p^2/2m $$ I don't understand how they...

I get that the impulse is I=FΔt, but why is it even equal to change in momentum caused by the force under consideration?

Is the following true if the momentum operator changes the direction in which it acts? \langle \phi | p_\mu | \psi \rangle = -\langle \phi |\overleftarrow{p}_\mu| \psi \rangle My reasoning: \langle \phi | p_\mu | \psi \rangle = -i\hbar \langle \phi | \partial_\mu | \psi \rangle \langle...

For part a, I have the following $$\ket{p_0} = \varphi_{p_0}(x)=\frac{1}{\sqrt{2\pi\hbar}}e^{ip_0x/\hbar}$$ but I am totally lost on how to proceed.

I am just solving the equation $$\frac{h}{2\pi i}\frac{\partial F}{\partial x} = pF$$, finding $$F = e^{\frac{ipx2\pi }{h}}C_{1}$$, and$$ \int_{-\infty }^{\infty }C_{1}^2 = 1$$, which gives me $$C_{1} = \frac{1}{(2\pi)^{1/2} }$$, so i am getting the answer without the h- in the denominator...

p=Bqr and del p = p del theta

we neglect gravity and viscosity efects i really can't understand how does the author managed to get the equation in the image

1/2mv^2 = 1/2mv^2 - 1/2kx^2 but can't plug in numbers for x or m mv+mv=mv+mv but no mass given very lost

I don’t understand how energy is conserved here. The energy of the atom when n=5 is -.544eV. The energy of the photon is 1.14eV. After release, the energy of the atom is -.544 - 1.14 = 1.68eV. Using this value, I get n = 2.67, not an integer, so n = 3 and the atom has energy = -1.51 eV. I...

I looked in the instructor solutions, which are given by: But I don't quite understand the solution, so I hope you can help me understand it. First. Why do we even know we are working with wavefunctions with the quantum numbers n,l,m? Don't we only get these quantum numbers if the particles...

So if i have a photon of some energy and i want to find the magnitude of the momentum, i can get the right answer but the units don't make sense. So i derive p = E/c since i know the energy of the photon and i used f=E/h and substituted this into p=hf/c This means for units of the equation p...

Hi all, If a body has a given initial momentum and then travels through a continuously less dense medium would it's velocity increase to conserve momentum? Thanks Jerry

First, introduce the energy – momentum equation E² = p²c² + (m0c²)². Next, just think it in natural way. If the energy – momentum equation reflects the stationary situation, then, momentum p naturally equals to zero. Then, we got E² = 0 + (m0c²)², namely: E = m0c². It can be denoted exactly...

i. Rearranging the equation for kinetic energy in terms of momentum; 1/2mv^2=(mv)^2/2m=p^2/2m Inputting the values given KE=1^2/2*4kg = 1/8 J Kinetic energy of a body with twice the momentum; KE=2^2/2*2kg =1 J The ratio of the kinetic energy of the first body to the second body is therefore...

t is Torque I is the inertia moment P is the power c is the constant light speed r is the spot distance to the fiber p is the torsional constant theta is what we want In the equilibrium $$t = 0$$ $$ F\Delta T = \frac{E}{c} = \frac{P\Delta T}{c} => *F* = \frac{P}{c} (1) $$ This will be the...

m1 + m2 = 8 COE 0.5(m1)(u1)^2 + (m1)(g)(30) + 0.5(m2)(u2)^2 + (m2)(g)(30) = 0.5(m1)(v1)^2 + 0.5(m2)(v2)^2 + (m2)(g)(16) Can you check if my eqn is correct? And can you advise what to do after this? I wanted to do COLM but i don't know what is the initial part.

When A hits B, COLM mV = -mVa + 2mVb V = 2Vb - Va COKE 0.5mv^2 = 0.5mVa^2 + 0.5(2m)Vb^2 V^2 = Va^2 + 2Vb^2 When B hits C COLM 2mVb=4mVc Vc = 0.5Vb COE 0.5(2m)Vb^2 = 0.5kx^2 +0.5(4m)Vc^2 sub Vc = 0.5b mVb^2 = KX^2 After that I am stuck, cause i can't find V in terms of Vb only

Hello! Would it be possible to brake a magnet by means of short circuiting a coil placed at the end of a plastic tube where the magnet has been accelerated in ? Is there a conversion of magnet speed to electric current/energy inside the braking coil ? It is thaught for reusing the projectile...

Okay, i know that as a ball collides with a pivoting rod on an axis, the ball has angular momentum. Therefore after the collision, the ball is stopped or slowed, and the rod swings. The ball provides a force and torque to the rod. But if I isolate the ball, isn't the only thing acting on the...

Question 1: Since Force=Change in momentum = ∆P / ∆t = mv / t Momentum of the water coming out=mv mv=ρVv=ρAv Force d/dt (ρAv2t)=ρAv^2 Force = 1000*40*30ms^2 Force = 3.6*10^7 N Question 2: This is where I am confused because I understand in an elastic collision total kinetic energy and...

Is it correct to say that that τ=0 since r has the same directacion as F?? and for \vec{L} que need to find \vec{p} So I thought solving this dif equation ## \int dp/dt =−kq/r^2 +β^4/r^5## Do you agree in the path I am going?

In this question, the particles are constantly transmitting their momentum to the rocket. The force required to keep the rocket stable can be express as ##\vec F=(\vec v-\vec u)\dot m##. However, when I tried to solve this question using the Newton's 2nd law, I found that the infinitesimal...

Hi, I was trying to derive relativistic momentum equation using classical momentum equation but it didn't work. Could you please help me? Thank you! Where am I wrong? Or, is not possible, in any way, to derive relativistic momentum using Newtonian momentum equation? Thanks!

HI τ= r ˆr x - ##k / r ^ 2## ˆr= 0 right? since ˆr x ˆr is zero What about L?

$$\hat{T}_{\mu v}(x)=e^{i\hat{P}x}\hat{T}_{\mu v}(0)e^{-i\hat{P}x}$$, so $$\bra{\overrightarrow{P'}}\hat{T}_{\mu v}(x)\ket{\overrightarrow{P}}=e^{iP'x}\bra{\overrightarrow{P'}}\hat{T}_{\mu v}(0)\ket{\overrightarrow{P}}e^{-i\hat{P}x}$$ Now, $$\partial^{\mu}\Phi=\int\frac{d^3 k_1}{2\omega_{k_1}...

So, what I did was suppose the mass of ramp is $ M_r$ and let velocity at B of block be v, then, after inellastic collsion both bodies v' velocity at B , $$M\vec{v}= M_r \vec{v'}+ M \vec{v'}$$ or, $$ \frac{M}{M +M_r} \vec{v}= \vec{v'}$$ Now, Suppose I take the limit as mass of ramp goes to...

I was first wondering wether we can solve this question by applying conservation or energy or not but after googling it I found that we can't apply conservation of energy since there will be some energy lost in this case. I don't know how this energy is getting lost. My second doubt was if we...

We know that photons (light) are massless but they have momentum. Now suppose I am in the space far away from planets/stars that there is no external force exerts on me, if: 1- I turn on a flashlight (torch), would I be pushed in the opposite direction which the flashlight is facing (Newton's...

Summary:: Would energy method give us a different answer from conservation of angular momentum? Hello, I do not know how to type equations here. So, I typed my question in Word and attached it here. Please see photos. Note: This question is not a homework. I did not find it in textbooks or...

I was wathcing a video about radial velocity method for seeking exoplanet(video) and on 3:05 author writes that momentum of a star equal momentum of a planet. Why?

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For the region where V = 0, solving the schrodinger equation leads to the above value of wave function, psi = sqrt(2/L) sin(pi x/L) Since in the qus. it is not stated about the 'direction of movement' only restricted to +x direction, I think that the probability will be 1/2. And finding the...

In which coordinate system the components of angular momentum are quantized? Better to say, if we can select the coordinate system arbitrarily, how the components of angular momentum, say z-component, are always ##L_z=m\hbar##?

(just a illustrative picture)

Let's say you have two masses on either side of a spring. Mass 1 is connected to the end of a spring. The spring itself has no mass. Mass 2 is free in space. So you have: [M1]-[spring] [M2]So it's more descriptive, I'll name the variables like you might in programming. Let's define...

A gun is fired vertically into a block of wood(unknown mass) at rest directly above it. If the bullet has a mass of 24.0g and a speed of 310 m/s, how high will the block rise into the air after the bullet becomes embedded in it?

I read the Wiki page https://en.wikipedia.org/wiki/Electron_cyclotron_resonance as well as this answer here How does a cyclotron work? and it describes a setup where one has a cyclotron which has a static magnetic field pointing up through the dees and there is an alternating high voltage...

I first got the velocity of the combined mass with conservation of momentum and as it was in the mean position the velocity can be written as v = wA ( w= angular frequency , A = amplitude ) as we have to take it back to natural length i put A as the initial extension but i am getting a wrong ans...