Momentum Definition and 1000 Threads

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F =...

[Mentor’s note: moved from the technical forums so no template] A turntable with a moment of inertia of 5.4x10-3 kgm^2 rotates freely with an angular speed of 33 1/3 rpm. Riding on the rim of the turntable, 15cm from the center is a cute, 32g mouse. a) If the mouse walks to the center of the...

I have transformed the incoming colliding objects to the zero momentum reference frame as shown in the diagram. I want to calculate the angle ##\kappa##. I don't understand how to do that. But here is what I have so far. $$u_{com} = \frac{m_1u_1 + m_2u_2}{m_1+m_2}$$ where ##u_1,u_2## are the...

I have two streams that impinge upon one another as shown in the diagram. Stream 1 with mass flow rate of ##m_1## and velocity of ##u_1## impinges upon Stream 2 with mass flow rate of ##m_2## and velocity of ##u_2##. This results in flow in the forward (f) and backward (b) direction of the x...

So far I’ve dealt with scenarios in which the vehicle colliding with the rear of the other vehicle ‘joins’ the other vehicle, and the ‘two become one’, so there is one final velocity. Why have these two vehicles not ‘become one’? I’ll have a go at the maths first then have a go at answering...

consider this situation. The diagram I have drawn is just after the smaller mass m begins sliding. So first thing I wanted to do is define my system. Here I have defined my system as "Small mass m+ Larger wedge M". DOUBT 1: I had a rather silly idea- is it right to consider the "floor" as part...

So my first approach was to use L=Iw. Computing I, moment of inertia,I=$$I_{center} = \frac{md^2}{4}$$ $$L_{center} = I_{center} \omega = \frac{md^2\omega}{4}$$ And hence I obtain an answer. However, when I further thought about the question, I realised that L is a vector and I can probably do...

My classical mechanics is very rusty. Recently, I wondered if it is possible to replace the canonical momentum with the kinetic momentum using a canonical transformation (so this isn't homework). I tried to work this out, but somehow, the Lorenz force got lost. Maybe some of you has an idea what...

Hi all, When we hold the hammer at the top of the handle, we can swing faster compare to when we hold the hammer at the bottom of the handle. Let say one holds the bottom of the handle(12 in long) of a 100g hammer vs one holds the middle of the handle(12 in long) of a 200g hammer. Do they...

Heisenberg uncertainty principle relates to the limitations on the precision with which certain pairs of physical properties (like position and momentum) of a particle can be simultaneously known. The uncertainty relations for position and momentum as operators arise from the non-commutative...

Let the velocity of the wall be ##u## Since there is no impulse in the vertical direction, the vertical motion of the ball is unaffected by the collision. I proceeded by working in the frame of the moving wall, therefore the ball now Initially has : ##V_x = 8 + u ## ##V_y = 6## For the ball...

A question states that a ball with a mass of 5 kg and a velocity of 10 m/s collides with a stationary wall. The question then asks for the momentum of the ball after the collision. No other information is given. This is a rather ambiguous question, as it doesn't provide the time taken for the...

(a) $$\bar x=\frac{\int_{0}^{L} \frac{\alpha_o}{L}x^2dx}{\int_{0}^{L}\frac{\alpha_o}{L}xdx}$$ $$=\frac{2}{3}L$$ (b) $$x=\frac{x_1+x_2}{2}=\frac{1}{6}L$$ $$y=\frac{y_1+y_2}{2}=\frac{1}{3}L$$ (c) I am not sure about this part. Do I need to divide the conservation of momentum into two...

Hi everyone, I am not sure if I have calculated task b correctly: The Lagrange function has the form ##L=\frac{1}{2}m\Vert \dot{\textbf{x}}\|^2+\frac{q}{c} \dot{\textbf{x}} \cdot \textbf{A}-q\phi## I then formed the canonical momentum ##\pi=\frac{\partial L}{\partial \dot{\textbf{x}}}##...

Suppose I have an initially localized free particle at x0 then I measure its momentum it will become a plane wave so there is a probability that if I measure its position again to find it far away from its initial position if the time between the two measurements were T isn't finding the...

Let the representation of a Hermitian Operator in some basis ##x## be $$\hat A\equiv A(x)$$ and let $$\psi(x)=\langle x\vert\psi\rangle$$ Then we define $$A(x)\,\psi(x)=\langle x\vert\hat A\vert\psi\rangle$$ This is the Wikipedia article that mentions this. From here how do we derive the...

I'm trying to understand if I'm making a mistake because the answer in the textbook is ##10.2~km/s##. Here's my attempt at a solution: The subscript A is intended to mean apogee and P is for perigee. ##v_A = 3~km/s## ##w_A = \frac{v_A}{r_A} = 7.5 \times 10^{-5}~rad/s## ##L_i=L_f## ##I_Aw_A...

I was reading this A-level mechanics book by L. Bostock and S. Chandler. The chapter was momentum and in it, there's a section about instantaneous impulse. It says "There are many occasions when a force acts for so short a time that the effect is instantaneous, example a bat striking a ball, in...

Got an email today proposing naming the unit of momentum for Emmy Noether. It would be either the noether or the emmynoether: some people feel it is important to emphasize her gender. My understanding is it would not be SI, but US-only. Rereading the enail, it might not even be MKSA; I suppose...

I get the impression that momentum, in most physics questions (at least at GCSE level), is instantaneous. Is that correct? I tried to apply the basics to a walk to the local shops that I take regularly Distance 0.9 miles Time taken 0.25 hours Avg S=D/T Avg S=0.9/0.25 Avg S=3.6mph Avg...

Could someone please explain, in terms of the momentum, a rail car slowing down if an item is dropped vertically downwards on to it. Thanks.

Suppose in the presence of an electric field we solve electronic Hamiltonian with eigen energies and corresponding eigenstates ##|\psi\rangle##. The action of momentum operator on the stationary states ##|\psi\rangle## doesn't change by time. So, momentum-change (or acceleration) seems...

I figured since ## dr/dt ## is simply the velocity of the target mass, the velocity ##u_x## would simply have to be changed by the Lorentz transformation. Since the rest mass doesn't change, I think this should be as simple as taking the Lorentz transformation for velocity, and substituting the...

Somebody, please explain to me about the Lorentz force between two parallel current-carrying wires in terms of the momentum conservation as the electromagnetic fields has momentum density. Especially, (1), If a short rectangular magnetic pulse due to an electric pulse in one wire will still...

Does the time to the collapse of a particle system depend mainly on its mass/momentum, or complexity? For example macroscopic object. If system is quite isolated, is no spontaneous collapse even massive or complex systems?

Hello, I actually solved this problem using conservation of angular momentum, but I was wondering if linear momentum is conserved. Here's my thought process: (block + tile system) The block is going to hit the tile with some force ##\vec{F}##. Due to the Newton's third law, that force is also...

Hi, I'm working on part a of the following mechanics problem from MIT Open Courseware: https://ocw.mit.edu/courses/8-01sc-classical-mechanics-fall-2016/resources/mit8_01f16_pset9/: I think the key to solving this problem relies on the conservation of mechanical energy. Since there are no...

This isn't exactly a homework question, but it was inspired by a homework problem. It's my first time here, so if there's a better place for this question feel free to point it out. Let's consider a ball rolling up the following circular slope. Let's assume it rolls up the slope until it...

I'm confused on this problem, as I feel they state two completely contradictory things in the explanation of how to solve it. The first statement that I feel contradicts the second is this: "We can see that the bullet’s speed v must determine the rise height h. However, we cannot use the...

I'm trying to make a very basic physics engine. So far I've got a variety of small things worked out but I've been driving myself crazy trying to work out collisions. From one sense I get I can use momentum and impulse to determine the velocity of an object after a fully elastic collision (no...

I started checking for angular momentum conservation. The initial state has ##J_{in}=S_{\phi}=1##. The pions in the final state all have 0 spin, so the total angular momentum in the final state comes only from orbital momentum. Call ##L_{\pm}## the orbital momentum of the charged pions orbiting...

The first equation states that every wavefunction can be written as a sum of wavefunctions of definite momentum, with A_p being defined as the coefficients in the expansion such that when you take the |wavefunction|^2 it equals 1 - fine. We then multiply by the wavefunction conjugate and...

My textbook says the correct answer for #79 is 1551 kg but I get 1600 kg. I just attempted to solve it using conservation of momentum. Can't see where the math is incorrect.

I am studying particle pair production using Parker and Toms book: Quantum Field Theory in Curved Spacetime. On page 48 they talk about converting the sum over momentum (k) into an integral. You assume boundary conditions so that k = 2*Pi*n/L, where n is an integer and L is the coordinate...

Hello. I am reading Classical dynamics of particles and systems(Book by Stephen Thornton), I have problem in understanding the coordinate system they choose to define angular momentum for a rigid body. At the beginning of the chapter 11 they say: They use 2 coordinate systems to describe motion...

I am sorry I can't seem to get the LaTex to work $$\textbf{My question:}$$ A car collides with a fast-moving bus, which vehicle experiences the greater change in momentum? I am seem to get different answers on the internet: Chegg says both the same, quora says car, brainly says car, some...

Can someone share a paper or chapter from a textbook if they know a good one? I'm curious to see the explicit form of these matrices. In position space, the generators of boosts act on the rapidity, which can be related to velocity in X. Assuming the generators of boosts in K act on rapidity in...

TL;DR Summary: orbital speed laws I would appreciate a bit of explanation on how did we find e1 and e2 and if there are any useful references to learn about Kepler laws since I am lost for the most part, and would like to gain understanding and solving ability ,and if you can go into some...

I am not able to use Latex for some reason. It is very glitchy and if I do one backspace then it fills my whole screen with multiple copies of the same equation. Thus I am pasting a screenshot of handwritten equations instead. Apologies for any inconvenience. In Introduction to Quantum...

C. There is no net change in force, momentum, or velocity of the sail craft because the fan exerts a forward force on the air; however due to Newton's third law the air exerts an equal and opposite force on the fan. This air then exerts a forward force on the sail which cancels out the rearward...

As someone who only knows elementary physics (so pardon me for maybe getting some things wrong), I have a question which troubles me and I'm having difficulties in finding an answer to: If a plane takes off at the equator and flies east to west, counter to earth's rotation, how it would be able...

If one stands on a large planetary body, like the moon, and throws a large object, like a rock straight up, the object will leave with some velocity, slow down to a stop, and then come back down with the same velocity once it returns to its origin. In Newtonian mechanics, the understanding is...

Hello, I invite you to watch this video. This is a simple experiment, which has never been carried out and which proves that momentum can undergo a 'repartition'... The Beauty of Momentum What do you think of this phenomenon ? What conclusion can we draw from this? Thanks a lot for your answers.

##\vec{\rho_{D1,i}}+\vec{\rho_{D2,i}}+\vec{\rho_{D3,i}}+\vec{\rho_{R,i}} = \vec{\rho_{D1,f}} +\vec{\rho_{D2,f}} +\vec{\rho_{D3,f}} +\vec{\rho_{R,f}}## ##\vec{0} = \vec{\rho_{D1,f}} +\vec{\rho_{D2,f}} +\vec{\rho_{D3,f}} +\vec{\rho_{R,f}}## ##\vec{0} = m_D(15\hat{i} + 5\hat{j}) + m_D(-12\hat{i} +...

##m_s## = mass of snow ##V_s## = volume of snow ##\vec{v}## = velocity of snow D = density of snow ##\rho_{avg} = \frac{\rho}{V_s}## ##=\frac{m_s \vec{v}}{V_s}## ##=\frac{V_s D \vec{v}}{V_s}## ##=D \vec{v}## ##=350 \frac{1,000}{5.5}## ##=63,636.4## The textbook's answer is ##1.3 \times 10^9##...

So in my textbook there's a basic problem where you solve for the final velocities of two hockey pucks, which happen to have different colors which are red and blue, using conservation of momentum. The notation that the textbook uses to express the final velocities of the pucks is ##v_{1,f}##...

(bottom graph relates only to c) (a) i. The students can calculate the area under the graph to find the impulse exerted on the block. This is because the area under a force vs. time graph is the change in momentum or the impulse. ii. Knowing that the graph is linear and begins at around 3 N...

This effect is (apparently) always explained in terms of a "book-keeping" need to conserve angular momentum. I totally get that (as the kids say these days), but it doesn't provide a chain of cause and effect that leads to the observed rotation of the iron rod. Is there a classical thought...

I am stuck with this problem. Intuition tells me the answer is no, but I am struggling to prove it. If we consider two particles travelling in the same direction, the 2nd particle will gain velocity (impulse is in same direction to velocity), and the first particle will lose velocity (if it...