# What is Momentum conservation: Definition and 231 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.

View More On Wikipedia.org
1. ### 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...
2. ### 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...
3. ### 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...
4. ### 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...
5. ### 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 -...
6. ### 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...
7. ### 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...
8. ### I Unified Field Theory

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...
9. ### 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
10. ### 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...
11. ### 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...
12. ### 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...
13. ### 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...
14. ### 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...
15. ### 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

17. ### 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...
18. ### 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...
19. ### Momentum conservation in SHM

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...
20. ### 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...
21. ### 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:)
22. ### 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?
23. ### 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...
24. ### 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} =...
25. ### 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...
26. ### Momentum conservation equations

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
27. ### 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...
28. ### 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...
29. ### Find the magnitude of V1'

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.
30. ### 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...
31. ### 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...
32. ### 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...
33. ### 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...
34. ### 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...
35. ### 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...
36. ### 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...
37. ### B The physics of a Zipline

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...
38. ### 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...
39. ### 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...
40. ### 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...
41. ### 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...
42. ### Momentum conservation: block-wedge problem

Homework Statement A block of mass m slides down a wedge of mass M and inclination theta from rest. All the surfaces are smooth. Find the speed of the wedge when the speed of the block w.r.t to wedge is v. Homework Equations V(c.m.)=m1v1+m2v2/(m1+m2) The Attempt at a Solution Conserving...
43. ### Analyzing Elastic Collisions w/ Conservation of Energy and Momentum

Homework Statement There is a 4 kg mass that has a speed of 6 m/sec on a horizontal frictionless surface. The mass collides head-on and elastically with an identical 4 kg mass initially at rest. The final speed of the first 4 kg mass is: (a) 0 m/s (b) 2 m/s (c) 3 m/s (d) 6 m/s Homework...
44. ### Momentum Conservation: Ball Hitting Pivoted Rod

If a ball hits a rod at the top which is pivoted at bottom end then is linear momentum conserved?
45. ### A and C collide with B inbetween; AB elastic, BC inelastic

Homework Statement Three bodies A,B,C on frictionless surface masses= 1 kg each, Positions at time 0: A is at x=0,. B is at x=1, C is at x=2 (unit is 1 meter). velocities at time 0: A : 1m/s (to the right), B = 0 m/s, C = -1 m/s Assume sizes are uniform, or just ignore the sizes in...
46. ### Conservation of momentum - with understanding

I just want to state that i DID solve the problem. I just seek understanding of it. I'd be really grateful if someone could answer two of my questions at the end of this post. The problem I've solved here is just to show what I'm dealing with. 1. Homework Statement Object 1 is moving towards...
47. ### I Momentum w/o Net Velocity? Exploring the Lorentz Factor

(I hope this post doesn't cross the border into the forbidden realm of quackery and speculation.) I have what seems like a simple question about Special Relativity but I haven’t seen it discussed anywhere, nor has anyone I've asked. Does the nonlinearity of the Lorentz factor provide a way...
48. ### Maximum amount of energy the neutron can lose

A 1 keV fast neutron (relative mass 1) in a moderator collides elastically with a helium atom He (relative mass 4) at rest. What is the maximum amount of energy the neutron can lose? My answer is 16/25 of 1ke but while deriving this answer I simply solved based on the question as if the...
49. ### Momentum conservation

I read that kinetic energy may not be preserved, but momentum must always be preserved. How can that be? If there's a loss in kinetic energy due to friction or heat, the velocities will be reduced thus momentum will be reduced?
50. ### Two spheres of are dropped to ground while in contact.

Two spheres of different masses are dropped to ground.They are in contact as one above the other and are of masses, let’s say m and 2m.They are dropped with velocity v - My question is if we can conserve momentum and if we can why?And how to find the final velocity of upper ball after...