# Momentum Definition and 1000 Threads

In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If m is an object's mass and v is its velocity (also a vector quantity), then the object's momentum is

p

=
m

v

.

{\displaystyle \mathbf {p} =m\mathbf {v} .}
In SI units, momentum is measured in kilogram meters per second (kg⋅m/s).
Newton's second law of motion states that the rate of change of a body's momentum is equal to the net force acting on it. Momentum depends on the frame of reference, but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry.
Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is generalized momentum, and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle.
In continuous systems such as electromagnetic fields, fluid dynamics and deformable bodies, a momentum density can be defined, and a continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids.

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1. ### I [Q] Lorentz force in momentum conservation view

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...
2. ### B Does Particle System Collapse Depend on Mass, Momentum, or Complexity?

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?
3. ### Is Linear Momentum Conserved in This Case? (sliding box hits a floor tile)

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...
4. ### Conservation of Mechanical Energy - Which Equation To Use?

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...
5. ### Question About Momentum: Ball Rolling up a Curved Ramp

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...
6. ### Conservation of Momentum Problem - Mechanical and Kinetic Energies

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...
7. ### B How to determine applied force when two objects collide? (basic physics engine)

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...
8. ### Consider the hypothetical decay of the Φ(1020) meson into 3 pions

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...
9. ### Quantum - Postulate of getting specific momentum p = |A_p|^2

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...
10. ### Classical Mechanics: Rocket Propulsion Calculation

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.
11. ### A Converting momentum sums to integrals in curved spacetime

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...
12. ### Problem in understanding angular momentum of a rigid body

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...
13. ### B A car collides with a bus, who experiences a greater change in momentum?

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...
14. ### I The generators of a Poincare-type'' group in momentum space

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...
15. ### Using Kepler's laws to calculate elliptical planetary motion

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...
16. ### I How to "derive" momentum operator in position basis using STE?

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...
17. ### Blowing Into Your Own Sail

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...
18. ### B Inertia and flying

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...
19. ### I Is momentum conserved as a body falls through a gravitational field?

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...
20. ### B The inclined plane paradox (proved)

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.
21. ### Velocities of four masses | Conservation of Momentum

##\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} +...
22. ### Average momentum of an avalanche

##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##...
23. ### B More convenient mathematical notation for a simple use case

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}##...
24. ### How Does Impulse Relate to Momentum Change in Physics Problems?

(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...
25. ### I What Causes the Einstein - de Haas Effect in Iron Rods?

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...
26. ### Can Two Particles Have Multiple Collisions in a Single Interaction?

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...
27. ### Fast and Furious Scene Analysis

The collision seems to be an inelastic collision meaning momentum is conserved however, energy is not due to likely thermal energy from the collision. Using conservation of momentum, we can maybe somehow find the initial momentum of each vehicle and set it equal to the final momentums? However...
28. ### British physics olympiad problem: A ball bearing bouncing off a steel cylinder

I am struggling to find correct approximation for the problem. Is momentum conserved at the immediate impact of... (1) Can I ignore gravitational force and potential for the spring which is connected to ground and vertically upholding a mass . ( using equilibrium)
29. ### B Ignoring the motion of the Earth for energy vs. momentum conservation

Hi. If I drop an inelastic body, its potential energy first gets converted to kinetic, then to deformation energy. We use conservation of energy without taking into account the kinetic energy gain of the earth during the fall. However, at first sight conservation of momentum seems to be...
30. ### I Maxwell's equations and the momentum of charge

There appears to be a conservation of charge momentum (qv) analogous to that for mass (mv) although in the case of charge it is more potential in nature. A change in the flow of charge (or current) produces changing magnetic and electrics fields according to Maxwell's equations. These in...
31. ### I What part of momentum moves the boat in the inclined plane paradox experiment?

Hello and thank you for welcoming me to your forum! To get started, I would like to give you a little help: In the pattern experiment, when firing the cannon, if part of the momentum reaches the bird, and if another part of the momentum manages to stun the fish, what part of the momentum would...
32. ### B Does shortness from length contraction have a real physical effect?

Do the contractions affect physics in any frame? Examples: If length contraction reduces mass in the direction of motion, and therefore reduces the total momentum. (from observer's perspective) If in the reference frame of a station, the moving train weighs less than it did when parked...
33. ### How Do You Solve for Final Velocities in Elastic Collisions?

So i started off breaking up the problem into two sequences, right before the collision and after the collision has happened. I need to find the first ball's speed immediately before the collision which is no problem. PEi = KEf > mghi = (1/2)mvf (vf being the velocity right before the collision...
34. ### What was the mistake in solving for the speeds of two marbles after a collision?

Solved equation 1 for v1f and then substituted into equation 2 and solved for v2f. Got 2.22 as the answer, but it said the answer is incorrect.
35. ### Conservation of momentum for a robot on a space platform

The momentum of the robot is 95.0 x 1.4 m/s towards the platform. This must be equal and opposite to the momentum imparted to the beam. Dividing 133 kg m/s by 330.0 Kg gives a velocity of 0.403 m/s for the beam. So the relative velocity of the robot relative to the platform is 1.40 - 0.403 =...
36. ### I About the use of nominal definitions in physics

Hi, I was reading the interesting lecture of Feynman about Characteristics of Force -- https://www.feynmanlectures.caltech.edu/I_12.html He basically says that nominal definitions like mathematical definitions of "abstract" objects have actually no physical meaning. For instance take the...
37. ### Expected value of momentum P in terms of k

Now if I'm given a ##\phi(k)##, and I'm asked to find ##\langle p \rangle##, ##\langle p^2 \rangle##, etc. Am I justified to say that ##\langle p \rangle = \hbar \langle k \rangle## and that ##\langle p^2 \rangle = \hbar^2 \langle k^2 \rangle## ?
38. ### Rocket propelled by a beam of photons

Before the engine is switched off: $$P_{Initial rocket} = (m_{i}c, 0)$$ $$P_{photons} = (E/c, -p_{photons})$$ where E is the energy of the photons and ##p_{photons}## is the 3 momentum of the photons. Rocket after engine switched off: $$P_{Final rocket} = (m_{f}c, m_{f}v)$$ By conservation of...
39. ### Using Momentum Principle to Find Ratio of Speeds?

Given that the ions are initially at rest my initial velocity is 0. Therefore my Vavg is equal to vf/2 Using the formula Vavg = Change in positon/time, I can solve vf to be equal to 2r/t. Using the momentum principle, I get an equation of 2r/t = FnetT/12m -> Given that the mass of the ion is...
40. ### Attempting to teach this: Momentum and Impulse

For question 1. I am stuck. I know that the equation involves time and possibly rate, should solve for distance. But not sure how to set it up with information given. 2. Ft= m 🔺️ v F(3)= (100kg)(30m/s) 3 s= 3000 kg m/s Same applied to question 3. 3. F(2)= (100kg)(-30m/s) F(2) = -3000 kg m/s...
41. ### Change in momentum: Child jumping from a swing on a playground

800 - (32 x 9.8) = 32v/0.18 where v = velocity this gives me v = 2.736 m/s The answer given, however, is 800 = 32v/0.18, i.e. v = 4.5 m/s The difference, of course, is the weight of the child. I don't understand why this is not allowed for in the net force acting on the child. Can someone put me...
42. ### Why is momentum equal to mass times velocity?

I tried searching on the internet for hours to find an answer, but I didn't find any.
43. ### I Question about the velocity of the center of mass reference frame

I'm looking into center of mass and I saw the derivation of: ## V = \frac{\sum\limits_{i = 1}^{n} m_iv_i}{\sum\limits_{i = 1}^{n} m_i} ## I understand how it's derived, so no need to explain this further. It's a velocity of the frame in which total momentum of our objects is zero. Forget...
44. M

### Spring momentum conservation problem

For this problem, The reason why I am not sure whether it is a valid assumption whether momentum is conserved because during the collision if we consider the two masses to be the system, then there will be a uniform gravitational field acting on both masses, and a spring force that is acting...
45. ### B What will be the ball's velocity after a perfectly elastic collision?

From the bus driver's point of view, who is at rest, the ball's initial velocity is ##u+v##. After the collision, its velocity has to have the same value, but an opposite direction, so ##-(u+v)##. So that means that relative to me standing on the ground at rest, the ball's new velocity is...
46. ### Why Isn't Momentum Conserved with Varying Disk Radii?

Here is question + drawing.
47. ### I Why momentum is conserved when a gun fires? (conceptual question)

I understand that conservation of motion comes from the action and reaction pairs of newton's third law. When it is triggered, two forces appear that cancel when analyzed as a system. My question is how is it that momentum is conserved if before the shot there was no force in the system and...
48. ### I Can We Accurately Measure Momentum in the Lab?

In the lab, how accurately can we measure momentum? What is the max value of the uncertainty in position as the uncertainty in momentum approaches zero? Or vice versa. What experiments do these types of measurements?
49. ### I Angular Momentum problem v2 (mass moving inward or outward)

Hello, simplified the Angular momentum problem that comes up when i try to solve a mass moving inward or outwards and it does not conserver the angular momentum properly. I have tried this is many software by now, or by someone else and we all have found that there is no angular momentum...
50. ### Why is the thrust equation same under gravitational force?

The homework statement isn't exactly as is mentioned above. The actual problem statement is as follows: This is problem 3.8 from John R. Taylor's Classical Mechanics; however, my question is not related to the main problem itself but one particular aspect of it. Now, in the same textbook (John...