# What is Momentum conservation: Definition and 240 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. ### Trying to Calculate Initial Velocity and Final Velocity

1/2 mv^2 kx^2 1.2(0.15)v^2 = 1/2 (3)(0.05)^2 0.075 v^2 = 0.00375 V^2 = 0 00375 / 0.075 V^2 = 0.05 Initial Velocity = 0.7071 m/s I tried to calculate this one. I think for final velocity I should be using the slope? Any help would be appreciated thank you!
2. ### Failed rocket problem (momentum conservation, Kleppner 4-4)

Hi, Can anyone hint me if there is issue in the problem statement? Consistent answer can be obtained if one presumes that the trajectory of center mass is parabolic. Assuming this, the CM will land at distance L right to the axis of symmetry of parabola. But the problem tells about a rocket...
3. ### I Energy and momentum of a photon in a medium

According to this paper: https://academicjournals.org/article/article1380534636_Salih.pdf, the researcher states that energy of a photon is dependent on a medium while momentum of a photon is independent. However according to https://arxiv.org/ftp/physics/papers/0607/0607094.pdf, the research...
4. ### Momentum Physics Problem: Two astronauts throw billiard balls that collide

My attempt is shown below.
5. ### Would conservation of momentum apply in this vehicle accident homework problem?

Vehicle A Before collision = (mass of driver + mass of vehicle A) x velocity = (50+1000) x 20 =21000kgm/s After collision = (mass of driver x v) + (mass of vehicle A x 0) =50v +0 =50v 50v = 21000 v=420m/s Vehicle B Before collision = (mass of driver + mass of vehicle B) x velocity = (50+500) x...
6. ### What is the right formula to use in this context? (momentum conservation)

First i think the correct solution to the problem is But my friends argue that it is not what i did , i am confused we didn't see the whole chapter on momentum in class, (Youtube thank you) here is what my friends say : (0.3×5) + 0 = (V×0.3)+(0.4×2) and they get they a final speed of 2.33...
7. ### 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 =...
8. ### 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...
9. ### Golf club 🏌️and ball ⛳ impulse problem

I have done the first two parts of this question. ✅(i) Find the clubhead's change of momentum. ( dp = p_f - p_i = (0.225*18 - 0.225*30) = -2.7 kg ms^-1 ) ✅(ii) Find the impulse given to the golf ball. (F dt = dp = 2.7 Ns from part (i) with just a change in the units. Because of the...
10. ### Find velocities when a mass leaves a system of a rod with two masses

First, I can say that the velocity of the mass leaving the system is equal to ##w_o## (k) x ##L/2## (i) which tells me that its velocity will be w_o L/2 (j) Now, since the net external force is equal to 0, (linear) momentum is conserved, so: At first the velocity of the center of mass was 0 and...
11. ### Solving Elastic Collision of Two Balls: Theory & Solutions

With given information in the problem I can't decide which direction balls will go after collision. I assumed they will go in opposite directions. I know that is not a full solution, but I can't come up with anything else. From conservation of energy we have...
12. ### Solving Orbital Speed with Energy & Angular Momentum Conservation

I've already solved the orbital speed by equating the kinetic and potential energy in the circle orbit case. $$\frac{1}{2}mv^2 = \frac{1}{2}ka^2.$$And so $$v^2 = \frac{k}{m}a^2$$Now when the impulse is added, the particle will obviously change course. If we set our reference point in time just...
13. M

### Puck collision with rod using angular momentum conservation

For this problem, Why for part (a) the solution is, Is the bit circled in red zero because since the putty is released at a very small distance above the rod it velocity is negligible? Also for part (d) the solution is I did a computation of the initial and finial kinetic energies of the...
14. ### Conservation of Momentum of Rocket Exploding after Takeoff

-Solved for vf using equation 3 to get 20.0m/s (speed before explosion) then solved for the distance to reach the explosion using equation 4, to get 20.0m, which felt wrong having the same numbers but that may just be coincidence. -Found the distance travelled of the lighter piece using 530m -...
15. ### I Momentum of a Water Jet Impacting Plate

Suppose you have a jet of fluid (say water) traveling vertically upward at a constant velocity. It impacts a stationary horizontal plate and so moves radially outward in all directions. Assume that there's no energy loss during the impact, so the speed of the fluid remains constant. Is momentum...
16. ### I Kepler's second law derivation from angular momentum conservation

Many texts state that in an elliptic orbit you can find angular momentum magnitude as $$L = r m v = m r^2 \frac {d \theta} {dt}$$ I wonder if $$v = r \frac {d \theta} {dt}$$ is valid at every point. I understand this approximation in a circumference or radius r but what about an arc...
17. ### I Is a Unified Field Theory the Key to Understanding the Universe?

Is there any approach in any books out there, where we consider that in universe exists only one field, let it be called the Unified Field (UF), in which all of the known fields (gravitational, EM field, quark field, gluon field, lepton field, Higgs Field, e.t.c.) are just components (pretty...
18. ### 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
19. ### 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...
20. ### A bullet collides perfectly elastically with one end of a rod

A bullet with mass m, velocity v perfectly elastically, vertically collide with one end of a rod on a slippery plane and the bullet stops moving after the collision. Find the mass of the stick M the bullet stops moving after an elastic collision, so all energy is transformed to the rod. There...
21. ### 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...
22. ### I Can I suck myself forward with a straw when floating in air?

I find myself in a space with air but no gravity. Say at ISS. Can I suck myself forward by sucking a straw? It reminds me somehow of Feynman's sprinkler. Also Mach looked at something like Feynman's sprinkler. Mach invented something alike. Four ex/inhalers of air, tubes, that are in/exhale air...
23. ### Momentum in different referance frames

I aready got the solution for this exercise. However, the solution used the referance frame from the car: What I'm trying to understand is the line: Because before reading the solution, I was trying to solve it using the lab frame. So this is my work so far: Using conservation of momentum and...
24. ### Momentum Conservation: How to Reconcile a Negative Value?

Maybe a silly question but on the above question using the conservation of momentum: momentum before firing (0) = momentum after firing (55*35)+(M*2.5) If I re-range the above it's M = -(55*35)/2.5 = -770kg. I can I reconcile that minus sign (basically get rid of it)? Thanks

26. ### Conceptual questions about Angular Momentum Conservation and torque

List of relevant equations: Angular Momentum = L (vector) = r(vector) x p(vector) Angular velocity of rotating object = w(vector), direction found using right hand rule. Torque = T(vector) = dL(vector)/dt I have a few questions about torque and angular momentum direction and...
27. ### Application of momentum conservation in inelastic collisions

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...
28. ### Understanding Momentum Conservation in Simple Harmonic Motion

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...
29. ### Relativistic energy and momentum conservation

Summary:: this is what I've done so far... i don't think it works since i believe the information given is not even enough. the formula I've used are 1. relativistic total energy = rest mass energy + kinetic energy (line 1, 3) 2. conservation of energy (line 4, 7, 8, 9) 3. conservation of...
30. ### Hard Momentum Conservation Impact Problem

I believe momentum conservation is to be used in this sum since there's no external force, but I am not sure how to write the equation. Can someone please help me out:)
31. ### Is there a proof about angular momentum conservation?

Angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved). There is a proof about this conservation?
32. ### Angular Momentum Conservation in Spacecraft Orbits

Tell me if I'm right: A) Angular momentum is conserved because there are no external torques. Linear momentum isn't conserved because gravity is acting on the spacecraft . Mechanical energy isn't conserved because it has to change between different orbits. B) Parabolic orbit...
33. ### Momentum conservation for a free-falling body in GR

Hello everyone! It seems I can't solve this exercise and I don't know where I fail. By inserting the metric on the lefthand side of I. and employing the chain rule, the equation eventually reads (confirmed by my notes from the tutorial): m\frac{\mathrm{d}p_\delta}{\mathrm{d}t} =...
34. ### Laser beams interacting with a screen | AM and momentum conservation

a) On the black part, all incoming light is absorbed. This means that the momentum of the left-light beam doesn't change (i.e. momentum before hitting the black screen is ##\vec p_0## and after hitting it is zero. Thus ##\Delta \vec p = \vec p_0##). If momentum doesn't change, we get no...
35. ### Is My Solution to the Momentum Conservation Equations Correct?

I attached a PDF file where it clearly show the question and I showed my solution because trying to type it here will be quite hard I want to check if my solution is correct
36. ### A uniform rod allowed to rotate about an axis and then it breaks

A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...
37. ### Gauge pressure in Momentum conservation of fluids.

I want to ask why is it that we use gauge pressure instead of absolute pressure in CV analysis for momentum conservation of fluids. I did read that because P(atm) would be present everywhere so it won't have a net effect on the CV but it's highly non intuitive as I can't apply force balance on...
38. ### Calculating Momentum and Energy Conservation in Elastic Collisions

I know how to solve along x and y-axis but i can't think of how to start solving in the dricection on m1.
39. ### I The Symmetry of Angular Momentum Conservation

I suppose that the principle of conservation of angular momentum holds also for a cloud of particles weekly interacting at low pressure, density and temperature. And it should be still applicable when the particles or the atoms would start condensing and forming fusion products or simply solid...
40. ### Equalization of velocity components and momentum conservation

Hi, I understand and I'm sorry that there are going to be many loopholes in what I'm trying to put together and that too without any mathematical formulation but I don't even know where and what to start with. Suppose we have a finite length insulated hollow cylinder filled with with air at 1...
41. ### A question regarding energy and momentum conservation

I have a problem in mechanics. On the wedge and block only the gravisational force (mg) is exerted (and there is no friction in this system). What is asked in the question is the final velocities of the wedge and the block (vB, vK). The velocity of the block is conserved when it reaches at the...
42. ### Rotating physicist and momentum conservation

We are aware of the well-known problem of a rotating physicist whose angular velocity ω increases as a consequence of angular momentun conservation (##I_1 \omega_1 = I_2 \omega_2, \Sigma \tau_e = 0##). I am assuming that the net external force (##\Sigma F_e##) is also zero along with the net...
43. ### Angular momentum conservation and center of mass

Homework Statement Two bodies with an equal mass of M are attached by a pole with no mass with a length of L. The system is placed on a horizontal table and at first it is at rest. At t=0 a bullet with a mass of m hits the pole, as described in the picture. The collision is completely elastic...
44. ### Energy and momentum conservation

Homework Statement An object with a mass of 5kg is placed on a horizontal surface and it has a semi-circular orbit with radius 1m. Its left end is close to a baffle fixed on the ground. A ball with a mass of 1kg is released from the point A by static. The surface and the groove are both smooth...
45. ### Forces - Space Shuttle Takeoff Calculations

Homework Statement [/B] The total mass of a space shuttle and its launch vehicle is M=2000t. a) What must be the minimum size of the thrust force, to make the rocket move? b) The actual thrust of the rocket is F=30MN. What is its acceleration in the beginning? c) Assume that a mass of a...
46. ### B Can I Apply Physics Concepts to a Zipline Ride?

Hey! I am new on the forum and I joined because I really enjoy physics but I have a horrible teacher. I was wondering if anyone could help me on a question how do I find the velocity at the end of the zipline? how do I find the momentum of the object going down the zipline after it is...
47. ### Angular momentum conservation in collision with a nail

Homework Statement A ball of mass ##m## is attached to a massless string of length ##L##. The ball is released from rest as shown in the figure and as it reaches the bottom of the circle, the string wraps around a nail which is a distance ##d## below the center of the circle. What is the...
48. ### Conservation of angular momentum

Homework Statement A rod of length D sits at rest on a friction less table. A ball of mass M strikes the end of the rod with a speed V and rebounds with a speed 3v/4 causing the rod to rotate counterclockwise around a fixed axis at one end. The rotational inertia of the rod is I Homework...
49. ### Other I can't solve questions related to conservation of momentum

I'm a passout from school taking a gap year. I find the concept of conservation of momentum exceedingly difficult. Each question - and sometimes each part of a question, if a question has different parts - requires us to choose different systems each time. I look at the solution, and think I...
50. ### Real life problem about angular momentum conservation

Homework Statement suppose you're sitting on a rotating stool holding a 2kg mass in each outstretched hand, if you suddenly drop the masses, will your angular velocity increase, decrease or remain the same? Homework Equations dL/dt=net torque when net torque is 0, L=constant=Iw therefore...