# What is Linear momentum: Definition and 336 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. ### Collision between asteroids

Before the collision, the total linear momentum of the system is ##p = mv##, where ##m## is the mass of the minor asteroid and ##v## is its velocity. The total angular momentum of the system is ##L = mRv##, where ##R## is the radius of the major asteroid. Since there are no external forces or...
2. ### AP Physics C Mechanics: Linear Momentum for Colliding Billiard Balls

I'm guessing this question can be solved using the law of conservation of momentum Vi = 5 m/s (5 m/s) M = (4.33 m/s) cos30 M + V sinθ M I don't know what to do after this... I'm also not sure if I use the sin and cos correctly.
3. ### Electromagnetic linear momentum for a system of two moving charges

When you write out the equations of motion for a system of two isolated charges, you can add both of the equations and get the increase in the particles linear momentum on one side. On the other side, you get the sum of all the forces between the particles. I understand that this sum of forces...
4. ### I Summing linear momentum in circular rotation

Hello everyone! I was wondering why can't we take a rotating body and see the linear movement that each particle moves to find the 'total linear momentum,' I imagine this quantity would be conserved, and furthermore couldn't you write the total linear momentum as a function of angular velocity...
5. ### I How to account for linear momentum in a collision?

Suppose a bar is fixed to an axle at one one so that it can pivot. The bar is initially motionless, but is set rotating about it's axle when impacted by a ball. (The ball does not strike the bar at it's pivot point.) Suppose the collision is such that the bar is set rotating and the ball is...
6. ### Conservation of linear momentum, undergrad particle dynamics

Hi all, I'm opening this thread because of my uncertainty in how to correctly approach this exercise. My first thought was that, since the plate is subject to friction with the floor, it is going to stop, thus the final moment is 0. Hence, from the conservation of linear moment: m_Av_A+\sum...
7. ### Linear momentum of the Klein Gordon field

The correct answer is: #P = \int \frac{dp^3}{(2\pi)^3}\frac{1}{2E_{\vec{p}} \big(a a^{\dagger} + a^{\dagger}a\big)# But I get terms which are proportional to ##aa## and ##a^{\dagger}a^{\dagger}## I hereunder display the procedure I followed: First: ##\phi = \int...
8. ### Conservation of Linear Momentum of Rigid Body

I solved it by two methods: ----------------------------------------------------- First, by conservation of linear momentum, using the vector velocities of each particle: In the imminence of the impact, the velocity of all the three particles are the same, \vec v_0 = - \sqrt{2gh} \hat j...
9. ### Linear momentum problem with n particles

To find the mass in other pan, i need to find the force caused by beads on the pan ∴ KEinitial + PEinitial = KEfinal + PEfinal 0 + mgh = ½ mv^2 => v = 3.13 m/s ∴ The change in momentum : p2 - p1 = m ( v2-v1) = m( v - (-v)) = 2mv ∴ F = Δp / Δt = n. m. v How can i apply the rate of 100...
10. ### I Why does a cyclotron only impart linear momentum?

I read the Wiki page https://en.wikipedia.org/wiki/Electron_cyclotron_resonance as well as this answer here How does a cyclotron work? and it describes a setup where one has a cyclotron which has a static magnetic field pointing up through the dees and there is an alternating high voltage...
11. ### Linear Motion and Linear Momentum

Linear Motion Equation to get the common velocity of the block and bullet just after collision: v2=u2+2gs, I set v=0 at max height of s = 0.004 m and g = -9.81 m s-2 I got u = 0.28 m/s Then I calculate the impulse of the block using formula J = mv - mu, where v=0 and u=0.28 m/s and I got J = 1.4...
12. ### 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...
13. ### Describing the second law of motion using linear momentum

Hi! This is a very simple question regarding terms of expressions. One law of motion is: F=ma Another, using L as the linear momentum, is: F = dL/dt If the first equation can be characterized (ignoring reference frames) as a "coordinate-based equation" (since is concerned with the second...
14. ### Conversion of angular momentum to linear momentum

The balls used in the game of lawn bowls are biased so that they travel in a curved path of decreasing radius. When a bowl in motion collides at a glancing angle with another bowl at rest, it -appears- to increase its velocity. Due to conservation of linear momentum the post-collision velocity...
15. ### Calculating theta from alpha: Tan(theta)=Cot(alpha)

After impact VCos(alpha) will be normal to the inclined, now i calculated for theta by using [ Tan(theta) = vCos(alpha)/vSin(alpha),. Tan(theta)= Cot(alpha) ]. I don't know how to solve further to get value of theta, according to book thta = alpha.
16. ### Linear momentum or Angular Rotation

I think the answer is ##\frac{mV}{M}## but I am not sure. Won't the cylinder tries to rotate due to the collision at one end? Is this anything related to Angular Momentum? The Answers given were,
17. ### Find the impulse exerted on the wedge by the ground during impact

Now, the net vertical impulse on the wedge should be zero. It's quite obvious from the figure that the ground will also exert an impulse of ##J cos 30°## on the wedge. But they've given the answer as ##J sin 30°##. They're wrong, right?
18. ### Linear Momentum - Bullet hitting pendulum

Solving using Linear Momentum: M vb2/2 = M g 2L vb = 2√(g L) m v = m v/2 + M (2√(g L) ) v = 4 M √(g L) / m Note: I see from the answers - that this is correct. -------------- Next, I tried to solve it via Energy conservation point of view. M vb2/2 = M g 2L vb = 2√(g L) m v2/2 = m v2/8 + k...
19. ### Conservation of Linear Momentum

Homework Statement This question was on a recent AP Physics 1 exam as a multiple choice; "Three air track gliders, shown to the right all have the same mass M. Gliders 2 and 3 are initially at rest. Glider 1 is moving to the right with speed v. Glider 1 collides with glider 2 and sticks to it...
20. ### Angular and Linear Momentum Problem

Homework Statement A system has a ball and a uniform rod. The rod is rotating about point X on a frictionless table until it strikes the ball. The rod stops and the ball moves away. Variables: Rod's mass: m1 Ball's mass: m2 Rod's original angular velocity: ω Ball's final velocity: v Rod's...
21. ### When the spring is maximally extended, find v_1f

Homework Statement A mass m_1, initially moving at a speed v_0, collides with and sticks to a spring attached to a second, initially stationary mass m_2. The two masses continue to move to the right on a frictionless surface as the length of the spring oscillates. At the instant that the...
22. ### Describing the translation and rotation of a square frame

Homework Statement Four equal discs of mass ocuppy the vertices of a square frame made by four rigid bars of length and negligible mass. The frame is at rest on a horizontal table, and it can move with negligible friction. An instantaneous impulse is transmitted to one of the masses, in the...
23. ### Freezing of water inside a hollow sphere which is rolling

Homework Statement If we have a hollow ball completely filled with water which is rolling without slipping on a horizontal ground. If the water freezes which of the parameter will remain unchanged- angular speed, angular momentum, linear momentum, kinetic energy, total energy Homework...
24. ### Simple Harmonic Motion with Linear Momentum

Homework Statement Homework Equations T = 2pi * sqrt(m/k) mv =m2v2 (LM)[/B] The Attempt at a Solution [/B] So T2 depends on the mass and not velocity. So i can find T2 = 2pi * sqrt([m/2]/k) For A2 , i know that the amplitude before any collision is 1/2m1v1^2 = 1/2kA1^2 so solving that, i...
25. ### Linear Momentum to Angular Momentum

Homework Statement A 10 g bullet traveling at 400 m/s strikes a 10 kg , 1.2-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door immediately after impact? Homework Equations p[/B]= mv L = Iω...
26. ### Momentum transfer from linear to angular motion

I am trying to create a momentum trap to calculate the velocity of a projectile when it hits the trap. It essentially consists of a plate if known mass at the bottom of a pendulum of known radius. When the projectile hits the plate, the degrees that the pendulum rotates are recorded. I believe...
27. ### Problem about an elastic collision between a rod and a ball at an angle

Homework Statement Homework Equations Conservation of linear momentum Conservation of angular momentum ##\frac{-v_{relative after collision}} {v_{relative before collision}}=e## where e is coefficient of restitution The Attempt at a Solution Components of velocity given as...
28. ### How to understand linear momentum?

I understand for linear momentum the measure of the dificulty to take a body to the rest. But when I do the next exercises, I find that it requires less force for one body compared to the other with same linear momentum. Can someone explain me what to understand in an intuitive way what to...
29. G

### Why is linear momentum not conserved or realistic here?

- This is the situation provided where it has to be demonstrated that linear momentum is not conserved or unrealistic. My assumptions are: there's no friction due to how Godzilla is moving, the sand is acting as a lubricant. Velocity is constant. This is an elastic collision. I also guess that...
30. ### Conservation of linear momentum in this system

A pet mouse sleeps near the eastern edge of a stationary, horizontal turntable that is supported by a frictionless, vertical axle through its center. The mouse wakes up and starts to walk north on the turntable. Is the momentum of the system constant? i understand that the initial momentum is...
31. C

### Conservation of Linear Momentum and Covariance

Homework Statement Assume two masses m1' and m2' are moving in the positive x-direction with velocities v1' and v2' as measured by an observer in S' before a collision. After the collision, the two masses stick together and move with velocity v' in S'. Show that if an observer in S' finds...
32. ### I Finite universe, quantized linear momentum, and the HUP....

Hi all, Yet another question: if the universe is finite, then linear momentum should be quantized (I assume in a similar manner to an infinite potential well since there are boundary conditions). My question is, then, if one computes a value for ##\Delta p## (momentum variance), is the variance...
33. ### Drag force on a cylinder in an air tunnel

Homework Statement Let's have a cylinder in air tunnel. The air is flowing around cylinder. I want to calculate a net force acting on the cylinder. Part of the incoming air hits the cylinder and its trajectory direction changes. For that reason we can see straight behind the cylinder lower...
34. ### Reynolds transport theorem derivation - linear momentum

I've managed to derive the form of Reynolds transport theorem as a bilance of linear momentum of the system: \left (\frac{\vec{\mathrm{d} p}}{\mathrm{d} \tau} \right )_{system}=\frac{\mathrm{d} }{\mathrm{d} x}(\int_{V}^{ }\vec{v}\cdot \rho dV)+\int_{A}^{ }\vec{a}dm+\int_{A}^{ }\vec{v}\cdot \rho...
35. ### Conservation of Linear momentum

Homework Statement A 500g putty ball moving horizontally at 6m/s collides with and sticks to a block lying on a friction-less horizontal surface. If 25% of the kinetic energy is lost, what is the mass of the block? Homework Equations initial (i) = final (f) m1v1+m2v2 = m1v1+m2v2...
36. ### Can someone explain the theory of impact of jets?

So I did this lab on momentum on jets and the theory is that "a force is applied on the plate due to change of momentum" the jet both impacted on a flat plate and on a hemispherical plate; now i understand that the greater the angle of deflection of the water jet, the greater the change of...
37. ### Linear Momentum Bullet

Homework Statement A bullet of mass 0.011 kg is fired at a speed of 850 m/s. It embeds itself in a man of mass 90 kg. a) Find the momentum of the bullet before it strikes the man. b) Assuming it takes 0.1 seconds for the bullet to come to rest after hitting the man, calculate the average...
38. ### Linear momentum in oblique collisions and generally

In an oblique collision my understanding is that linear momentum is conserved in all directions (x, y, normal, tangential). But in a constrained oblique collision, does this change? For example if we had a block lying between two frictionless surfaces with an angled face ( a slope on one face)...
39. ### Finding velocity of a piece after explosion

Homework Statement A firework of mass 1 kg is placed on the ground and ignited , the impulse created by the explosion causes it to move vertically upwards,after 4 seconds a second explosion takes place in air and the horizontal impulse forces cause it to separate into 4 identical pieces 2...
40. ### Conservation of linear momentum when wheels are included

I am not a student. This is not a homework question. I am a 64 year old man who wants to understand a principle of physics. Suppose there is a large block of matter, designated as m2, which lies on a flat surface that initially is at rest. At some point in time a small block of matter...
41. ### 2-D Linear Momentum, Collision Problem

Good evening! I'm having trouble completing an assignment related to inelastic collisions and momentum. Homework Statement Here is the statement: You are in great shape on this hot July morning. You are working as an intern for the Montreal Police (SPVM) Collision Investigation unit. You...
42. ### Angular Velocity in Linear Momentum Equation

m1v1 = m2v2 v = rω m1(rω)1 = m2(rω)2 m1ω1 = m2ω2 Does this make sense?
43. ### Change in linear momentum

Homework Statement A 15 000kg loader traveling east at 20km/h turns south and travels at 25km/h. Calculate the change in the loader's a) kinetic energy b) linear momentum Homework Equations ΔKE= 1/2mvf^2 –1/2mvi^2 Δp= mv2 –mv1 m= 15000 vi = 20km/h = 5.56m/s vf= 25km/h = 6.94m/s The Attempt at...
44. ### Conservation of Momentum Degrees of Freedom

Hi I have been dealing with a fluid mechanics pressure gradient problem and from a statistical view point I can see how it resolves itself but am puzzled as to how it can occur at the molecular scale from a conservation of linear momentum perspective if Momentum is a conserved quantity While...
45. ### Forces appearing on the pipe when a fluid flows in it

Hi, I study linear momentum. But I cannot understand enough that how can forces appear on a pipe when fluid flows in the pipe? Fluid have a momentum as m*v how can forces appear on the pipe. I cannot demonstrate the situation in my mind. How can I find a demonstration or a free body diagram for...
46. ### Question about conservation of linear momentum

Homework Statement [pardon my crude drawing] Say I have a ball that hits the a rod at rest pivoted around hinge A. The ball in the diagram is the solid black, and the rod is the thin line in the diagram and is rotating around the square-shaped hinge at the bottom. I am not an artist but...
47. ### Collision involving angular and linear motion

Homework Statement a small 0.199 kg block slides down a frictionless surface through height h = 0.608 m and then sticks to a uniform vertical rod of mass M = 0.398 kg and length d = 2.23 m. The rod pivots about point O through angle θ before momentarily stopping. Find θ. point O is at the end...
48. ### Linear momentum problem (ballistic pendulum)

Homework Statement A ballistic pendulum is a device that may be used to measure the muzzle speed of a bullet. It is composed of a wooden block suspended from a horizontal support by cords attached at each end. A bullet is shot into the block, and as a result of the perfectly inelastic impact...
49. ### Linear Momentum of system of two blocks

1. Homework Statement The problem is shown in the photo above. I would like to discuss part B. Homework Equations conservation of linear momentum The Attempt at a Solution the solutions say that we should have the following approach: Mb*vb = [Mb + Ms] * vFinal. Plug in the numbers and get...
50. ### Linear momentum - Bullet fired vertically

Homework Statement A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s, how high will the block rise after the bullet becomes embedded in it? Homework Equations 1. m1v1 +m2v2 = mfvf 2. x=xo +vot...