# What is Conservation of momentum: Definition and 752 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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28. ### Conservation of momentum?

Hi all, If a body has a given initial momentum and then travels through a continuously less dense medium would it's velocity increase to conserve momentum? Thanks Jerry
29. ### Conservation of momentum and energy problem

In an elastic collision, a 400-kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. The initial speed of the leading bumper car is 5.60 m/s and that of the trailing car is 6.00 m/s. Assuming that the mass of the drivers is...
30. ### Conservation of angular momentum and its counterpart for linear momentum

Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds! --------------------------- I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...
31. ### Cars Collide on a Hill, Conservation of Momentum

QUESTION: ----------- For the purposes of this problem, we will define the direction of Vehicle A's initial velocity as the positive direction: While driving on a road that is inclined at an angle of 10 degrees above the horizontal, Vehicle A and Vehicle B are in a head-on collision lasting...
32. ### I Does Conservation of Momentum & Energy Hold in the C.O.M. Reference Frame?

We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?
33. ### 2D conservation of momentum

I am unable to find any angle for which the horizontal and vertical components of the linear momentum are conserved. I have added an image of my attempt
34. ### Conservation of momentum — Water dropped from a firefighting airplane

I could not unserstand part d.Does problem ask about plane's speed immediately after it starts to drop water or after the water is dropped completely?
35. ### Conservation of momentum when a ball hits a wall

I think we can.Although the wall is not moving, it is just because the wall has a huge mass.As rhe law of the conservation of momentum states(suppose the ball hits the wall from the left), when the momentum decrease by J, the momentum of the wall increase by J, which means the momentum of the...
36. ### Conservation of Momentum involving Vf, elastic collisions

I tried solving it using this method and I got 12.5m/s, and assumed the collision was elastic. The answer is actually 6.32m/s [41.5 degrees counterclockwise from the original direction of the first ball]; the collision is not elastic: Ek = 12.1J Ek`= 10.2J I have absolutely no idea how the...
37. ### Conservation of momentum in a bullet-block-spring system

According to the first equation, the final potential energy is equal to the initial kinetic energy of the block. So that means that Vblok is the instantaneous speed of the block right before it moves to the right and compress the spring, right? But doesn't the second equation (The initial total...
38. ### Simple Canon Question (Conservation Of Momentum): Frame of Reference

Since Pi = Pf, 0 = MbVbg + McVcg I just need to express Vbg in terms of Vbc and Vcg (that is, I need to express the velocity of the ball relative to the ground in terms that I know/want to solve for): by reference frames: Vbc = Vbg + Vcg so Vbg = Vbc -Vcg Now I can sub in and solve 0 =...
39. ### Conservation of Momentum: Elastic Collision of Two Masses

I really want to know which answer is correct. I don’t really know if I should include velocities to the left as negative velocities in the equation. Is it -1 or 4.33? Please help! Thanks!
40. ### Conservation of Momentum vs Constant k for an Ideal Spring

I encountered a weird conflict between my thought process and that of author's solution in book: The common viewpoint of both of us were invoking conservation of energy of this SHM system But the author proceeds to solve it using conservation of momentum, taking the new mass added to system as...
41. ### Conservation of momentum and energy

So to start off, the piece that hits the ground first is the smaller piece. So I can form the equations where: where ##8(u_{8kg})= m_{1}v_{1}+m_{2}v_{2}## ##m_{1}+m_{2}= 8## After 2 seconds, ##30 = v_{1}(2)+\frac{1}{2}at^{2}## ##v_{1}= 5.2m/s## ##(30-16) = v_{2}(2)+\frac{1}{2}at^{2}## ##v_{2}=...
42. ### Laws of conservation of momentum?

Problem Statement: Are this 3 topics comes under laws of conservation of momentum? Relevant Equations: Are this 3 topics comes under laws of conservation of momentum? Are this 3 topics comes under laws of conservation of momentum: energy lost due to impact, inelastic impact, purely elastic...
43. ### Wet wheel and conservation of momentum

A cyclist coasts along a road, he drives across a small puddle of water, after which the wheels leave wet lines on the road. Now we concentrate our attention to the linear momentum of the water on a wheel. It decreases. Momentum is conserved, so what got the momentum that the water had?
44. ### Conservation of Momentum (Elastic Collisions)

Part (iii) is the part I am stuck on and is a 5 mark question. I have some idea of how to attempt it shown below momentum is conserved so mux = mvy + mvz (where ux is the initial velocity before the collision of ball x, vy is the velocity after the collision of ball y and vz is the velocity...
45. ### Orbital Slingshot and Conservation of Momentum Confusion

Hello, I am an undergrad and am in an introductory level astrophysics course. I have a bit of confusion that I didn't know where to get help from so I made an account here. Please let me know if I miss some common etiquette or something... I don't understand how the slingshot maneuver...
46. ### 2D conservation of momentum

My only issue is what this would look like. I can't draw a respective picture.
47. ### Determining position of an object after inelastic collision

Homework Statement A 39,000 lb truck A and a 3968 lb sports car B collide at an intersection. At the moment of the collision, the truck and the sports car are traveling with speeds vA = 70 mph and vB = 30 mph. Assume that the entire intersection forms a horizontal surface. Letting the line of...
48. ### Ballistocardiograph and conservation of momentum

Hi, once again I'm probably asking a question that is more about human physiology than physics (I recently asked a question that had to do with hearing). I found a (definitely too hasty) reference to a ballistocardiograph in a high school textbook. So I got curious about the way this apparatus...
49. ### Railway/Cannon - Conservation of Momentum HW Problem

Hello forum. I have a HW question that I don't fully grasp just yet. It was multiple choice and somehow I guessed the right answer based on the work I did complete, but I want to know how to get to the solution and which steps I'm leaving out. I'll follow the format to write out the...
50. ### Ice Skating conservation of momentum (conceptual problem)

Homework Statement Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as in Figure 7.11, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces...