What is Conservation of momentum: Definition and 756 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. S

    Conservation of momentum problem

    Homework Statement a 120g arrow moving at 75m/s strikes and sticks in a 3.63kg wooden block, initially at rest. If the coefficient of friction between the block and the table it sists on is 0.409, how far does the block slide before stopping? Homework Equations m1v1+v1+m2v2=m1v1'+m2v2'...
  2. D

    Conservation of Momentum with Friction

    Homework Statement A bullet of mass m = 6.32 g is fired into a block of mass M = 2.30 kg that is initially at rest on a rough surface. (The coefficient of friction is 0.28 between the block and the surface.) The bullet ends up stuck in the block, and together they slide across the surface...
  3. M

    Studying Conservation of Momentum in Shooting a Bullet

    Ok so I want to know if conservation of momentum can be applies in a case of shooting a bullet to the wall I am talking about in the x direction of course since gravity is an external force in the y direction so a let say I shoot a bullet in a straight angle to the wall so it has huge x...
  4. L

    Conservation of momentum of a bullet question

    Homework Statement A bullet is shot horizontally into a block suspended by two strings. The bullet remains embedded in the wood and the wood and bullet together suspend upward. a) Explain why the horizontal momentum of the bullet-wood system is conserved during the collision even though the...
  5. Z

    Question about the conservation of momentum?

    If I were to just spawn into a complete vacuum of space with no initial velocity (momentum). Disregarding the fact that I would die due to lack of pressure and oxygen, would I be able to move my arms or legs at all because I would have no place to take the momentum from?
  6. M

    Conservation of momentum: vertical shot

    Homework Statement A 0.028 kg bullet is fired vertically at 165 m/s into a 0.15 kg baseball that is initially at rest. How high does the combined bullet and baseball rise after the collision, assuming the bullet embeds itself in the ball? Homework Equations mv + mv = mv + mv The...
  7. M

    Conservation of momentum railroad car collision

    Homework Statement A railroad car of mass 27000 kg moving at 2.00 m/s collides and couples with two coupled railroad cars, each of the same mass as the single car and moving in the same direction at 1.20 m/s. (a) What is the speed of the three coupled cars after the collision? Homework...
  8. M

    Conservation of momentum of astronaut in her space suit

    Homework Statement An astronaut in her space suit has a total mass of m1 = 91.3 kg, including suit and oxygen tank. Her tether line loses its attachment to her spacecraft while she's on a spacewalk. Initially at rest with respect to her spacecraft , she throws her oxygen tank of mass m2 =...
  9. S

    Conservation of Momentum, Energy

    Homework Statement A bullet with mass 20 grams and velocity 100 m/s collides with a wooden block of mass 2 kg. The wooden block is initially at rest, and is connected to a spring with k = 800 N/m. The other end of the spring is attached to an immovable wall. What is the maximum compression...
  10. P

    Cart-Cart Collision, Conservation of Momentum

    Homework Statement A cart (m1 = 130 kg) is moving to the right along a track at v1i = 24 m/s when it hits a stationary cart (m2 = 350 kg) and rebounds with a speed of v1f = 4 m/s in the opposite direction. a) With what speed does the 350 kg cart move after the collision? A: 10.4 m/s An...
  11. Z

    How does the conservation of momentum explain this?

    Picture the Earth without any atmosphere or air molecules. If I were to throw a rock with 0.5 kg straight up from the surface of the Earth it will reach a velocity of zero at its peak? At this moment the momentum of the rock becomes zero. Where does the momentum go if its always conserved?
  12. e2m2a

    Euler's First Law and the Conservation of Momentum

    I know Euler's first law applies to a single body, but can we use it for a system of bodies? Or should we invoke the conservation of momentum to obtain the same result for a system of bodies?
  13. S

    Conservation of momentum and energy question

    Hello everyone, Let's say there was gun and a bullet with a mass of 1kg at rest. The bullet and guns speeds were 2 m/s in opposite directions after firing if I right the equations. Kinetic energy 0.5m1v12 + 0.5m2v12 = 0.5m1v22 + 0.5m2v22 Why doesn't this equation work when objects are at...
  14. stevmg

    Conservation of momentum a universal truth

    Wherever I have read, the conservation of momentum is a universal truth. This is the basis, as I undertsand it, to the mass equation: m = m0/SQRT(1 - v2/c2) in which m0 = the mass in the rest frame and m is the mass in the moving frame relative to the rest frame moving at v. The idea...
  15. M

    Conservation of momentum basics

    Two baseballs undergo a head-on collision. Ball 1 is twice as heavy as ball 2. Ball 1 is traveling at an initial speed of v1, while ball 2 had an initial speed of v2. Elastic collision. If ball 1 travels at a speed of 7/5v1 after impact, what is the speed of ball 2? Conservation of...
  16. H

    Work - energy theorem and conservation of momentum question

    Homework Statement There is a hemispherical track of radius R = 4m. A block B is lying at rest at the bottom of the track. A block A is pushed along the horizontal portion of the track with speed u. Collision between A and B is perfectly elastic. Find u such that B reaches P (the end of...
  17. A

    Law of conservation of momentum problem

    Homework Statement A falling rock gains momentum as its speed increases. Does this observation contradict the law of conservation of momentum. Explain. Answer in the textbook: This observation does not contradict the law of conservation of momentum. The momentum of the Earth increases...
  18. A

    Conservation of Momentum of a Star

    Homework Statement Iota Draconis is the eighth brightest star in the constellation Draco. Observations show that a planet, with an orbital period of 1.50 y, is orbiting this star. The mass of Iota Draconis is 1.05MSun. (a) Estimate the size (in AU) of the semimajor axis of this planet's...
  19. F

    Conservation of Momentum and Kinetic Energy in 2D Collisions

    Homework Statement Object A has a mass of 2.0 kg and an initial velocity of 2.5 m/s. It strikes Object B, which is at rest and has a mass of 2.0 kg as well. After the collision, the objects travel in different directions, with Object B traveling at an angle of 44 degrees from its...
  20. H

    Conservation of Momentum, again :/

    Homework Statement Valentina, the Russian Cosmonaut, goes outside the ship for a spacewalk, but when she is floating 15m from the ship, her tether catches on a sharp piece of metal and is severed. Valentina tosses her 2.0kg camera away from the spaceship with a speed of 12m/s. a.) How fast...
  21. H

    Conservation of Momentum of roller-skates

    Homework Statement Anthony and Sissy are participating in the "Roll-a-Rama" roller-skating dance championship. While 75kg Anthony roller-skates backwards at 3m/s, 60kg Sissy jumps into his arms with a velocity of 5m/s in the same direction. m1= 75kg v1= 3m/s m2= 60kg v2= 5m/s v' = ?Homework...
  22. M

    Conservation of momentum with a spring

    Homework Statement A spring with spring constant K is compressed by x and used to shoot a ball of mass m into an initially stationary block also of mass m. The ball sticks to the block after the collision. Calculate the final velocity of the ball + block. Homework Equations The...
  23. B

    Conservation of momentum, spinning disk

    Assumptions: 2D problem only, no gravity, no friction, no external torque. Flat circular disk spinning at a constant angular velocity w. Disk is initially at (0,0), but is NOT restrained in translation. Disk has some finite mass. A small ball (finite mass) is tethered to a string which...
  24. X

    Conservation of Momentum and linear momentum

    Homework Statement In which one of the following situations is linear momentum not conserved? A) A bomb suspended by a string explodes into one hundred fragments. B) A bowling ball collides with ten pins. C) A golf ball is struck by a club. D) An astronaut floating in space throws a hammer...
  25. G

    Conservation of Momentum Problem

    Homework Statement Objects A and C are made of different materials, with different “springiness,” but they have the same mass and are initially at rest. When ball B collides with object A, the ball ends up at rest. When ball B is thrown with the same speed and collides with object C, the...
  26. D

    Conservation of momentum problem (I think?)

    Homework Statement http://img14.imageshack.us/img14/5489/25765454.png A projectile is launched from a cliff above level ground. At launch the projectile is 35 meters above the base of the cliff and has a velocity of 50 meters per second at an angle 37° with the horizontal. Air resistance...
  27. N

    Conservation of Momentum of a boat and women

    Homework Statement I'm getting fairly frustrated seeing as I've been working on this 'easy' problem for several hours yet still can't get the correct solution. The problem is as follows: A 180 lb- man and a 120-lb woman stand side by side at the same end of a 300-lb boat, ready to dive, each...
  28. F

    High school algebra -> relativistic conservation of momentum and energy

    "high school" algebra -> relativistic conservation of momentum and energy Homework Statement Consider a head-on, elastic collision between a massless photon (momentum po and energy Eo) and a stationary free electron. (a) Assuming that the photon bounces directly back with momentum p (in the...
  29. M

    Conservation of momentum and mechanical energy

    (wasn't sure if I should post this in the general physics or in the "homework" forum... this question is loosely based on a problem found in a printed book, but I have modified it myself... regardless, here is the situation) Homework Statement A person is sliding down a frictionless...
  30. N

    Conservation of momentum problem

    Homework Statement Two boats move parallel each other inertially in opposite directions. They both have a speed of 6m/s. When they are near we move a load from one boat to the other. After this the second boat continues in the same direction with a speed of 4m/s. Find the mass of the second...
  31. H

    Can Conservation of Linear Momentum Estimate Velocities When External Forces Act?

    Conservation of linear momentum holds if no external net force acts on the system. Therefore we use them to calculate the velocities of objects after collison. However, my professor said that we can use the princple of Conservation of linear momentum to estimate the velocities of objects when...
  32. S

    Quick question on explaining the law of conservation of momentum.

    I have done the question already and attained the correct answer. However if it was a written question i do not know how i could prove the following. A 7.3 x 10^3 kg space vehicle and its empty 6.8 x 10^2 booster unit are moving together through space at 370 m/s. An explosion lasting 2.2s is...
  33. M

    Principle of conservation of momentum

    In a test laboratory, a car is crashed into a concrete wall and comes to rest. There is no damage to the wall. Explain of how the principle of conservation of momentum applies to this situation. Answer: The Earth plus car recoils with same momentum as the car had Why "the Earth" and not...
  34. P

    Conservation of Momentum - Shuffleboard

    Hi PhysicsForums. :P First time here. I would just like someone to verify whether I did this problem correctly. A moving shuffleboard puck has a glancing collision with a stationary puck of the same mass. If friction is negligible, what are the speeds of the pucks after the collision? Given...
  35. T

    Conservation of momentum - Brakes

    Not sure where to post this as it isn't actually homework, all variables are made up. Homework Statement A car, weighing 1000kg and moving at 3m/s puts it's breaks on and slows down to a stop. What happens to the momentum? Homework Equations p=mv The Attempt at a Solution...
  36. B

    Conservation of momentum with initial velocity of 0

    I'm having a bit of trouble understanding the concepts of momentum conservation. Let's say I'm standing on a frictionless surface and I throw a 3kg brick horizontally with a velocity of 4m/s. In this scenario I can see that I'm going to be repelled backwards at a velocity of 12/my mass in kg but...
  37. V

    Conservation of momentum multiple choice

    Here is the question 5. A long board is free to slide on a sheet of frictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causing the board to slide and rotate. In this situation, which of the following occurs? A) Linear momentum is...
  38. T

    Conservation of Momentum- Help with sources of erorrs?

    Hey everyone. In class, we conducted a lab to verify the law of conservation of momentum. On a frictionless surface (glass surface), we had to collide two masses and record the time, and then make calculations for the velocity... and using that, calculate the initial and final momentums and...
  39. J

    Conservation of momentum & energy

    Homework Statement A block of mass m1 = 2 kg slides along a frictionless table with speed 10 m/s. Directly in front of it, and moving in the same direction with a speed of 3 m/s is a block of mass m2 = 5kg. A massless spring with spring constant k = 1120 N/m is attached to the second block...
  40. S

    Conservation of Momentum in a 2D Collision

    Homework Statement Two masses, m1 = 4 kg and m2 = 12 kg, have initial velocities of v1i = 28 m/s [+x 35 +y] and v2i = [-y 60 +x]. If the first mass has a final velocity of v1f = 18 m/s [-y 40 +x], find: a). The final velocity of m2. b). Whether or not the collision can be said to be...
  41. putongren

    General Conservation of Momentum Question

    Hey All, I was looking at several conservation of momentum question, and one question caused me to thinking about something. In those planet versus satellite questions, a satellite passes through a moving planet and the gravitational pull of the planet alters the final satellite's velocity and...
  42. putongren

    Calculus conservation of momentum problem

    Hello All, I am trying to understand the solution of a problem that uses calculus and the conservation of momentum principle.The problem is here: http://www.physics.harvard.edu/academics/undergrad/probweek/prob79.pdf and the answer is here...
  43. M

    Conservation of Momentum, a Totally Inelastic Collision

    Homework Statement A 950kg compact car is moving with the velocity ⃗v1 = 32 ˆx + 17 ˆy m/s. It skids on an icy, frictionless patch and collides with a 450kg hay wagon moving with velocity ⃗v2 = 12ˆx +14ˆy m/s. If the two stay together, what is their velocity? Homework Equations...
  44. M

    Conservation of Momentum in a explosion

    Homework Statement A firecracker, initially at rest, explodes into two fragments. The first, of mass 14g, moves in the positive x direction at 48m/s. The second moves at 32m/s. Find the mass and direction of its motion. Homework Equations p=mv The Attempt at a Solution So I...
  45. M

    Inelastic Collision and Conservation of Momentum

    Homework Statement A student performs a ballistic pendulum experiment using an apparatus similar to that shown it the figure. Initially the bullet is fired at the block while the block is at rest (at its lowest swingin point). After the bullet hits the block, the block rises to its highest...
  46. A

    Conservation of momentum and relative velocity

    Homework Statement So you've got two people standing on a boat, everything at rest, and the masses of both people as well as the boat are known. Let's call them Richard and Sandra, so the variables are Mr (mass of Richard), Ms (mass of Sandra), and Mb (mass of boat). When one of these...
  47. C

    Conservation of Momentum homework help

    Homework Statement A 93 kg astronaut and a 1500 kg satellite are at rest relative to the space shuttle. The astronaut pushes on the satellite, giving it a speed of 0.16 m/s directly away from the shuttle. Seven-and-a-half seconds later the astronaut comes into contact with the shuttle. What...
  48. N

    Compton Scattering and Conservation of Momentum

    Homework Statement photon scatter angle is theta, electron recoil angle is phi prove tan(phi) = (1+hf/mc^2)^-1 cot(theta/2) Homework Equations The Attempt at a Solution Conservation of energy is the same as in here: http://en.wikipedia.org/wiki/Compton_scattering...
  49. E

    Conservation of Momentum Elastic Collision Problem

    Homework Statement I am basically being asked to use the law of conservation of momentum and kinetic energy to derive two equations for the final velocity of the two masses involved in the system. (i.e. \acute{v_{1}} and \acute{v_{2}}) Homework Equations Conservation of Momentum...
  50. T

    Mastering Physics Help, Conservation of Momentum

    Homework Statement A 238U nucleus is moving in the x direction at 4.5*10^5 m/s when it decays into an alpha particle 4He and a 234Th nucleus. 1.) If the alpha particle moves off at 34degrees above the x-axis with a speed of 2.0*10^7 m/s, what is the speed of the thorium nucleus? 2.)What...
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