# Momentum conservation Definition and 56 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. ### 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...
2. ### 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...
3. ### 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...
4. ### 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...
5. ### 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...
6. ### 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.
7. ### 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...
8. ### B The physics of a Zipline

Hey! im 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 deployed...
9. ### 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...
10. ### 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...
11. ### 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...
12. ### 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...
13. ### Conservation of momentum - need help 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...
14. ### I Can a system have momentum without net velocity?

(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...
15. ### 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...
16. ### 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...
17. O

### Energy Lost during elastic collision.

Homework Statement . True or False:[/B] For a completely elastic collision of two isolated masses the energy lost is ½μνr2 Where μ is the reduced mass of the system and νr is the magnitude of relative velocity between the two particles. Homework Equations The Attempt at a Solution Elastic...
18. C

### Apparent violation of momentum conservation in EM

We have two cylindrical shells (with radii a and b and charges +Q and -Q) along the z-axis. There is a uniform magnetic field (in the positive z-direction) out to radius r from the z-axis. Because of the symmetry, the total field momentum is zero. Suppose we now connect the shells using a wire...
19. ### How to find the resultant force in a T tube section

Homework Statement So, I need to find the X and Y components of the force in the T section Homework Equations Due the fact that the problem dosn't ask for a specific force I couldn't think in any other equation to use, because even tough there is Pressure and Gravity acting I need to...
20. ### Conservation of Momentum Problem

Homework Statement The same horizontal force is applied separately to two objects initially at rest on a horizontal, frictionless surface. Object A has less mass than object B. In each case the force is applied for the same length of time. Which of the following statements is true after the...
21. ### Collisions -- conceptual questions

Homework Statement Let two particles of equal mass m collide. Particle 1 has initial velocity v, directed to the right, and particle 2 is initially stationary. A: If the collision is elastic, what are the final velocities v_1 and v_2 of particles 1 and 2? B: Now assume that the mass of...
22. ### Conservation of momentum - Vertical spring

Homework Statement A block of mass 200g is suspended through a vertical spring. The spring is stretched by 1.0 cm when the block is in equilibrium. A particle of mass 120g is dropped on the block from a height of 45 cm. The particle sticks to the block after the impact. Find the maximum...
23. ### Elastic/Inelastic collision upon Traincrash

Homework Statement A railway waggon of mass m=20t is travelling with v=18km/h. It then hits 10 other stationary railway waggons, with each one having the same mass of m=20t . (Friction is not being considered) Homework Equations a) Assume the 10 railway waggons are connected through strong...
24. ### Momentum not conserved?

I remember throwing clay balls at walls in my childhood and observing them stick to the wall. In a more scientific perspective, considering the ball and wall as a system, I can say that the total momentum before collision is greater than 0. But then, after the collision, the kinetic energy of...
25. ### Conservation of Momentum with Friction?

When reading lessons on the conservation of momentum, you usually see examples with colliding balls or something to that effect. These examples always seem to fail to mention friction. These balls will always come to a stop due to friction. How is momentum conserved when it is lost to friction...
26. ### Sign convention problem in momentum calulations

Homework Statement Particle A has a mass of 1kg and velocity 2x10^8m/s to the right and collides with a stationary particle B that has a mass of 4kg. after the collision, particle A moves to the left with a velocity(v) and particle B moves to the right with a velocity of 1x10^7 m/s. calcuate...
27. ### A momentum question following collision

I think this is a basic question, at least I would hope so. If two identical motorcycles are going at the same speed but one has a lighter individual. If each individually collides with a stationary object and the driver is ejected. Who will go further and why?
28. ### I Is Canonical Momentum conserved?

Given a system of charged particles interacting with an EM field. Is the canonical momentum always conserved? If so, what is the associated symmetry? Thanks in advance.
29. ### Conservation of Momentum Spaceship Question

Homework Statement The mass of a spaceship is 10012 kg. The spaceship is at rest. Then one part of the ship with a mass of 1000 kg is ejected and emerges with a speed of 112 m/s. What is the speed of the other part? Homework Equations The Attempt at a Solution I tried: pi=pf mivi=mfv2...
30. ### Finding velocity and momentum of a bullet and recoiling gun

Homework Statement A bullet leaves the barrel of a gun with a kinetic energy of 90 J. The barrel of the gun is 50 cm long. The gun has a mass of 4 kg, the bullet 10 g. (a) Find the bullets final velocity. (b) Find the bullets final momentum. (c) Find the momentum of the recoiling gun. (d) Find...
31. ### I Why are some systems defined with the name "variable mass"?

I do not get why systems such as the rocket in space are defined as "variable mass" since the mass of the system is not varying. The equation used for such systems $$\sum F^{(E)}=\frac{d\vec{P}}{dt} \tag{1}$$ (sum of external forces on the system equals the change in momentum) holds true only...
32. ### Would momentum be conserved?

Would momentum be conserved on a cart if in one situation it is on an incline and the other it is on a flat surface(assuming it is pushed) I am confused because I thought that since gravity is an internal force, it is a conservative force. But then the final velocity of the cart would be...
33. ### Compton Scattering; Relation between scattering angles

Homework Statement Show that the scatter angles of the photon (θ) and electron (Φ) in the Compton effect are related by the relation: ##cot (θ/2 )=(1+\frac{hf}{mοC^2}) tan(Φ) ## Where f is the frequency of incident photon 2. The attempt at a solution I wrote down the equations of conservation...
34. ### (Tricky) Comet Picking up Mass - Differential Equations

Homework Statement A comet in deep space picks up mass as it travels through a large stationary dust cloud. It is subject to a gravitational force of magnitude Mf acting in the direction of its motion. When it entered the cloud, the comet had mass M and speed V. After a time t, it has travelled...
35. ### Momentum and push starting vehicles

Homework Statement This was a question I came across in my A level physics course: A garage attendant was surprised to be asked to give a lorry a push as the battery was flat. He was even more surprised when he leant on the back of the lorry and the slight movement of the lorry was enough to...
36. ### Tensile test failure velocity

Hi, so when doing a tensile test lets say on a threaded bar and a nut. The nut thread reaches failure and shoots off. How would you calculate that velocity and the actual force that it would hit say a wall 20cm away. just for information the failure point was at about 300kN
37. ### 2D Momentum Collision

Homework Statement One car of mass 1400 kg is travelling at 45km/h when it collides and becomes entangles with another car mass of mass 1300 kg travelling at 39km/h[E]. What is their velocity after collision So MA = 1400 kg VA = 45kh/h MB = 1300 kg VB = 39 kh/h [E] and After Collision: MAB...
38. ### A rod falling on a frictionless surface

Homework Statement Consider a massless rod of length $L$ with a small mass $m1$ attached on one end, and $m2$ attached on the other end. The rod is initially in the vertical position at rest on a frictionless surface, with $m1$ on bottom and $m2$ on top. A small impulse is applied to the top...
39. ### How do I figure out the final position of the block?

Homework Statement Three blocks of identical mass are placed on a frictionless table as shown. The center block is at rest, whereas the other two blocks are moving directly towards it at identical speeds v. The center block is initially closer to the left block than the right one. All motion...
40. ### 2D elastic collision

Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with angle 30° to the original path, determine: a. the speed of the first ball after the collision. b. the speed and direction of the second ball after...
41. ### Calculating angle of ball after collision

Homework Statement The white ball in the figure has a speed of 1.81 m/s and the yellow ball is at rest prior to an elastic glancing collision. After the collision the white ball has a speed of 1.37 m/s. To the nearest tenth of a degree, measured counterclockwise from east, what angle does it...
42. ### Momentum conservation in perfectly inelastic collision

Dear Experts, Total momentum of a system is said to be conserved in perfectly inelastic collisions also. I have a slight problem trying to comprehend a simple example regarding the same. If a small mass 'm' , say a ball is thrown at a huge stationary mass 'M' , say a wall. If the collision is...
43. ### Can conservation of momentum be applied here?

Take the case of Atwood machine, Where the masses of blocks are m and m,now,another ball of mass m strikes one of the blocks with a speed v and sticks to it. Considering our system as blocks+ball+string connecting the blocks(no pulley),can we apply conservation of momentum? Please explain...
44. ### Momentum Conservation

Homework Statement A car of mass 1500kg is parked on a 30degree slope before rolling down a distance of 30m onto a flat section where it collides with a stationary car. The cars stick together and scrape along the road for 20m until they come to a rest. Calculate the velocity of the two...
45. ### Force exerted on the palm of your hand by a beam of light

Compute the force exerted on the palm of you hand by the beam from a 1.0W flashlight. (a) if your hand absorbs the light, and (b) if the light reflects from your hand. What would the mass of the particle that exerts that same force in each case would be if you hold it at earth's surface? On...
46. ### Direction of particles after decay w/ relativity

One of the possible decay modes of the neutral kaon is ## K^0 \rightarrow \pi^+ + \pi^- ## The rest masses of the K0 and pion are 498 MeV/c2 and 135 MeV/c2, respectively. In 2-dimensions (xz-plane), if the kaon has an initial momentum of 2000 MeV/c in the z direction, what is the momentum of...
47. ### Law Of Conservation Of Momentum Help

Homework Statement A flywheel and shaft have a moment of inertia of 600kg and is rotating at 5 rev/s. Another flywheel and shaft, on the same axis, is suddenly connected by means of a clutch. If this flywheel and shaft has a moment of inertia of 620kg and is initially at rest, calculate: a)...
48. ### Elastic collision in 2-dimensions

Homework Statement A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball. If the first ball moves away with angle 30° to the original path, determine: a. the speed of the first ball after the collision. b. the speed and direction of the second ball after...
49. ### Venturi Vaccum increase in Momentum

I was hoping to get a more complete understanding how a Venturi vacuum increases the Momentum of the fluid. I know Momentum is an awful way to pose this question but it really is important that it can be explained by momentum instead of conservation - Hence the post. An initial pressure...
50. ### Finding the maximum compression of a spring

Homework Statement A block of mass m1 slides along a frictionless table to the right with a speed of v1. A second mass M2 slides in the same direction with a speed of v2 such that it will collide with m1 which is in front of m2. Say that a spring of stiffness k is attached to one of the masses...