What is Momentum: Definition and 1000 Discussions

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. C

    I Summing linear momentum in circular rotation

    Hello everyone! I was wondering why can't we take a rotating body and see the linear movement that each particle moves to find the 'total linear momentum,' I imagine this quantity would be conserved, and furthermore couldn't you write the total linear momentum as a function of angular velocity...
  2. M

    B Conservation of Momentum for system of particles

    We know that if we take two particles and assume no external force is applied then by Newtons third law total momentum gets conserved after collision. If we take three particles and there is collision between them and no external force then the momentum is again conserved for each pair like in...
  3. Diracobama2181

    A Off-Forward quark-quark amplitude in momentum space

    I am having difficulty writing out ##\bra{p',\lambda}\psi^{\dagger}(-\frac{z^-}{2})\gamma^0\gamma^+\psi\frac{z^-}{2})\ket{p,\lambda}## in momentum space. Here, I am working in light-cone coordinates, where I am defining ##z^-=z^0-z^3##, ##r'=r=(0,z^{-},z^1,z^2)##. My attempt at this would be...
  4. A

    B Conservation of momentum and conservation of energy details

    If we have a ball with mass m dropped from a height h down to the ground, how come we can't set the conservation of energy equation just as the velocity of the ball turns 0. mgh = 0 If instead the ball were moving with an initial velocity v, would the equation be ##mgh + \frac{1}{2}mv^2 = 0##...
  5. M

    B K Energy & Momentum: Driving Force or Lost Heat?

    https://www.physicsforums.com/threads/conservation-of-momentum-and-loss-of-energy-in-inelastic-collisions.311037/post-2182192 If I understand correctly mathematically the momentum of the system remains unchanged but individual momentums decreases always. In an inelastic collision the momentum...
  6. AspiringPhysicist12

    Conservation of momentum problem (sand-spraying locomotive)

    If I consider only the freight car's mass and the mass dm that's added to the freight car as part of the system, then I get this answer: https://ibb.co/QfKSqQ5 But if I consider the freight car's mass, the mass dm, and the locomotive car as part of the system (maintaining the locomotive has...
  7. V

    Angular momentum of a disk about an axis parallel to center of mass axis

    I am using the following formula to solve this problem. $$ L_a= L_c + \text { (angular momentum of a particle at C of mass M)}$$ Because the point C is at rest relative to point A, so the second term in RHS of above equation is zero. Hence, the angular momentum about A is same as angular...
  8. Y

    Momentum and impulse problem: A mass collides with another mass on a spring

    i would like to get some help and to understand why my answer is incorrect , here is how i did the first and second part. about the first part i did it right but i don't understand what I am doing wrong in the second part i tried -k and i get -23.997 and i also try +k and i get 23.997 but they...
  9. V

    Determining $L_{o}$: Finding Angular Momentum of System

    I think the the time given doesn't matter since no torque is acting on the system, but not sure. Therefore, all we need is to determine the angular momentum about the axis passing through O and perpendicular to the plane of disk. This will involve finding the moment of inertia of smaller disk...
  10. R

    I How to account for linear momentum in a collision?

    Suppose a bar is fixed to an axle at one one so that it can pivot. The bar is initially motionless, but is set rotating about it's axle when impacted by a ball. (The ball does not strike the bar at it's pivot point.) Suppose the collision is such that the bar is set rotating and the ball is...
  11. LCSphysicist

    Getting the Klein Gordon energy momentum tensor

    I want to get the stress energy tensor of a scalar field using the Hilbert method (namely, ##T^{\mu v} = \frac{2}{\sqrt{-g}} \frac{\delta S}{\delta g_{\mu v}}##) $$S = \int \frac{1}{2}(\partial_\mu \phi \partial^{\mu} \phi - m^2 \phi ^2)\sqrt{-g}d^4x$$ $$= \int \frac{1}{2}(\partial^{v} \phi...
  12. LCSphysicist

    Energy momentum tensor - off diagonal terms

    Let's arrange the rod's axis parallel to the z axis. ##T_{00} = A/\mu## (since it represents the energy density) ##T_{03}=T_{30} = \frac{F\sqrt{\mu / F}}{A}## (It represents the flow of energy across the z direction) ##T_{33} = F/A## (pressure) It seems that ##T_{33}## i have got has the...
  13. lola1227

    Momentum Collision Homework Problem -- help please

    Parallel: M1V1+M2v2=M1V1’+M2V2’ (0.5)(3)+0=(0.5)(cos60)(3)+V2’Cos(x)(0.5) V2’cos(x)= Perpendicular: M1V1+M2v2=M1V1’+M2V2’ 0=(0.5)(0.3)(sin60)+V2’sin(x)(0.5) V2’sin(x)= And the divide 2 by 1 Which is tan(x)=2/1 And then plug then back into solve, but I don’t think we do it like this because...
  14. dahoom102

    Momentum - Impulse collision to find initial speeds and directions

    Hi I've tried solving this question but it seems that I flipped the direction of the impulse, what did I interpret wrong? the question didn't give any clue on their direction before so I couldn't infer the direction of the impulse. It also just gave me the magnitude without the direction. I...
  15. G

    Momentum and Impulse Problem with a Ball bouncing off a Wall

    a) Assuming it is inelastic as it is accelerating and therefore kinetic energy is not conserved? Intuitively this doesn't feel right... b) change in momentum = p initial - p final = force x time p initial = 0 as at rest p final = 0.25 x v2 force x time = area under graph = 0.1 therefore 0.25 x...
  16. mohamed_a

    I Acoustic wave properties and momentum

    I have read about doppler effect in acoustics so i searched for the relation ship between wavelength of wave produced by linear movement of body and its momentum along with other dependent variables such as density of fluid (leaving acoustics for a second) and temperature but souldn't find a...
  17. Assaltwaffle

    I Question about transfer of Energy and Momentum in Ballistics

    My apologies if the prefix is too high of complexity. I don't know where this would fall, difficulty or academically speaking. While it may be surprising to some given Hollywood's portrayal of it in movies, if a person in wearing hard bulletproof armor is struck by a projectile, the person is...
  18. J

    I Impact, momentum, demand and capacity

    I'm struggling with trying to find how conceptually need demand and capacity to be conciliated during impact. In particular, I find two different formulas in papers and websites dealing with impact. In all cases, they state that there are two forces acting on objects on impact, where they...
  19. A

    I Conservation of angular momentum during collisions

    Hello everyone, I have a doubt regarding the conservation of angular momentum. When dealing with collisions between two objects, if the net external force is zero we know that the linear momentum is conserved; even when the system is not isolated, for instance because of gravity acting on the...
  20. J

    I Momentum, impact force and Earth

    Suppose two objects, A and B, with large lengths LA and LB, and masses MA and MB, collide at time t0. Both objects before collision are vertical and aligned concentrically, being object B positioned initially at a higher z coordinate than object A. The bottom end of object A is rigidly...
  21. coolpoke0908

    I Can someone explain why momentum does not commute with potential?

    My assumption is that knowing potential can lead to knowing the position, but I don't know how this can be.
  22. qsduahuw

    Angular momentum / conservation of momentum questions

    I thought the answer is B because the angular momentum in conserved in all 3 pictures. <Moderator's note: Use of external servers not allowed. Please upload all images to PF.>
  23. A

    I Conservation of angular momentum -- spinning a bicycle wheel in space

    Suppose we have a rotating body like a bicycle wheel in space away from gravity. This body stops after a while due to friction between the wheel and wheel axles. Is not the conservation of angular momentum violated?
  24. Anmol Dubey

    Calculating final rotational speed from angular velocity

    I have no idea how to go about this. Any help would be appreciated thanks :) Edit: I converted the 1.5 rev/s to rad/s = 9.4 rad/s
  25. J

    B Conservation of Energy and Momentum in an Explosion

    Hey, I have a question about explosions and how kinetic energy works during them. I have outlined my question on the attached image. Please let me know if something is wrong or needs clarifying. Thank you.
  26. Shreya

    Momentum Conservation: Bullet enters a block

    I can understand that using conservation of momentum, we can find v. But we need V for that. The equation for V involves h and so we need h. But I am not able to comprehend the equation involving l,h and a. The question doesn't specify what a is. Please be kind to help
  27. BranRubaba

    I EM waves have no mass but they do have momentum?

    I was studying radiation and came across an article: https://www.wtamu.edu/~cbaird/sq/2014/04/01/light-has-no-mass-so-it-also-has-no-energy-according-to-einstein-but-how-can-sunlight-warm-the-earth-without-energy/#:~:text=In summary, all objects with,not the only massless object. Which said...
  28. V

    Trouble with a Rocket Propulsion question (Variable Mass & Momentum)

    I chose to set the upwards direction to be positive and dM/dt = R = 190 kg/s, so I can solve the problem in variable form and plug in. With the only external force being gravity, this gives M(t) * dv/dt = -M(t) * g + v_rel * R where M(t) is the remaining mass of the rocket. Rearranging this...
  29. Christian Thom

    A Galactic Rotation and Energy-Momentum Tensor

    Galaxies are very large rotating bodies, so it seems that, as with the Kerr model for black holes, there could be an effect of this global rotation on the energy momentum tensor in the more dense regions of the galaxy that could in turn affect the space-time in the vicinity of the object and so...
  30. K

    I Position representation of angular momentum operator

    One of the component of angular momentum operator is ##\hat{L}_{x}=\hat{y} \hat{P}_{z}-\hat{z} \hat{P}_{y}## I want it's position representation. My attempt : I'll find the representation of the first term ##\hat{y} \hat{P}_{z}##. The total representation is the sum of two terms. The...
  31. D

    I Ideas about observing position and momentum at the same time

    I am very interested in quantum mechanics/physics and i keep seeing the Heisenberg uncertainty principle and its making me think about other forms of viewing particles. We traditionally use Photons to view something (our eyes), or other forms of radiation/particles, but i know that merely...
  32. S

    Conservation of momentum of spacecraft and asteroid

    By "DART will have a relative speed of 6250 ms-1 when it collides with the asteroid", I assume it is the relative speed of the DART with respect to the asteroid. Using that assumption, I can answer question (a) For question (b), I don't understand the solution from the teacher. He did it like...
  33. Yan Campo

    I Robertson uncertainty relation for the angular momentum components

    I'm studying orbital angular momentum in the quantum domain, and I've come up with the Robertson uncertainty relation for the components of orbital angular momentum. Therefore, I read that it is necessary to pay attention to the triviality problem, because in the case where the commutator is...
  34. K

    I Basic question on meaning of momentum operator

    How do we apply the momentum operator on a wavefunction? Wikipedia says > the momentum operator can be written in the position basis as: ##{ }^{[2]}## ## \hat{\mathbf{p}}=-i \hbar \nabla ## where ##\nabla## is the gradient operator, ##\hbar## is the reduced Planck constant, and ##i## is the...
  35. rudransh verma

    Bomb explosion -- calculating the momentum of one of the fragments

    I think if the two parts move in -x and +y direction, it must be balanced by the resultant of the two vectors but in opposite direction. So ##p\sqrt5## will be the answer. But I don’t think this is the right way to solve this.
  36. K

    I Finding Momentum Mean & Variance from Wavefunction

    I've a Gaussian momentum space wavefunction as ##\phi(p)=\left(\frac{1}{2 \pi \beta^{2}}\right)^{1 / 4} e^{-\left(p-p_{0}\right)^{2} / 4 \beta^{2}}## So that ##|\phi(p)|^{2}=\frac{e^{-\left(p-p_{0}\right)^{2} / 2 \beta^{2}}}{\beta \sqrt{2 \pi}}## Also then ##\psi(x, t)=\frac{1}{\sqrt{2 \pi...
  37. R

    I Why is momentum considered a vector and kinetic energy a scalar?

    I'm not interested in the mathematical derivation, the mathematical derivation already is based on the assumption that momentum is a vector and kinetic energy is a scalar, thus it proves nothing. Specifically, what happens if we discuss scalarized momentum? What happens if we discuss vectorized...
  38. A

    A Double-Slit Experiment: Momentum & Position

    In the double-slit experiment with two open slits, is there a fixed relationship between the momentum (p) of the particle immediately after passing through the slit and the position (q) of the impact on the screen?
  39. wheelman

    I How to transfer angular momentum between two flywheels?

    I am trying to build a simulation of a car engine and wheels for a game project. My model is currently this: Engine outputs a torque -> this spins up a flywheel over time (the physics step of 1/60s) -> the flywheel is coupled with the clutch and thus transmission -> the transmission multiplies...
  40. deFe_9807

    A Calculation of dipole and quadrupole momentum of CO

    This is my first post of this topic so I hope it is in the correct place. I need some help to figure out the using of GAUSSIAN in order of calculate the dipole and quadrupole moment for the carbon monoxide molecule with different levels of theory (SCF and Post Hartree Fock methods). In...
  41. rudransh verma

    B Understanding Momentum: The Relationship Between Mass, Velocity, and Force

    “Momentum is clearly a vector quantity. The following common experiences indicate the importance of this quantity for considering the effect of force on motion. 1. Suppose a light-weight vehicle (say a small car) and a heavy weight vehicle (say a loaded truck) are parked on a horizontal road. We...
  42. spacecadet11

    I General physics question -- How can massless photons have momentum?

    P=mv *momentum equals mass X velocity. Light particles or "photons" are said to be "massless". And yet they have momentum. How is that possible? (p.s. I used to know the answer)
  43. mohamed_a

    I Problem with understanding angular momentum

    I have a problem in understanding angular momentum equation (mrv), especially the part where radius is involved. imagine an elastic collision occurred between sphere of mass (M) attached to a string forming a circle of radius (R) and moving with velocity (V) and another stationary sphere having...
  44. I

    I Rotational Orientation of Monatomic Gas: Angular Momentum Effects

    In other words, is there a rotational orientation of each atom in a monatomic gas (and corresponding rotational speed conserving angular momentum) that affects collisions, or does a substance need to have at least 2 atom particles to have the orientation/rotational ability to have particle...
  45. P

    The velocity of a movable block that is penetrated by an arrow

    This problem is in a chapter on momentum in the book basic engineering mechanics explained. Help me Mario
  46. Ineedhelpwithphysics

    Conservation of Momentum problem — Firing a cannonball

    So I am guessing the cannons final velocity will be 4 m/s to the left because there momentum before shot was 0 because of opposite and equal reaction so 50,000kg x -4 m/s + 20kg x 10,000 m/s = 0 ?
  47. S

    Kepler's Third Law vs Conservation of angular momentum

    The classic way to go about this problem would be to use Kepler's laws and thus find the new time period of earth. However I encountered this question in a test on rotational motion which deals with conservation of angular momentum. The equation used here would be I1ω1= I2ω2 Replacing I with MR2...
  48. E

    I Momentum conservation for EM-Field/matter interaction

    Hello, I'm reading Feynman Lectures Vol II, and saw this "paradox" in section 26-2 (Figure 26-6), where two orthogonally moving charges can be shown to have unequal action and reactions. Later in Chapter 27, the explanation was given briefly citing field momentum. I tried to prove this...
  49. mattlfang

    Perfectly inelastic collision of two moving and rotating disks

    two moving and rotating, uniformly weighted disks perfectly inelastic collide. The disks are rotating in opposite directions (see the diagram) At the moment of their collision, the angles between their velocity and the line connecting their centers are 45 degrees. The velocities are therefore in...
  50. greg_rack

    Engineering Solving Momentum Conservation Problems: Tips & Tricks

    Hello guys, could someone give me a small hint to get me started on attempting this problem? I really cannot figure out how to relate conservation of momentum to the fact that there shouldn't be friction... does it have something to do with the so-called "sweet spot" of the ball? But then...
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