# Momentum Definition and 422 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 Pulling cable through underground ductwork.

Hello all, I am an Engineering dropout turned Cable Splicer. In my job we do a lot of Heavy Duty underground cable pulling. Usually plastic jacketed cable through some type of ductwork (typically plastic as well). We use a winch truck and a heavy rope to pull this cable through the ducts...
2. ### Velocity of a relativistic particle in a uniform magnetic field

d(ɣmv)/dt = qvB (dɣ/dt)mv + ɣm(dv/dt) = qvB Substituting gamma in and using the chain rule, it ends up simplifying to the following: ɣ^3*m(dv/dt) = qvB Now, I am confused on how to solve for v.
3. ### Momentum Collision Homework Problem -- help please

Parallel: M1V1+M2v2=M1V1’+M2V2’ (0.5)(3)+0=(0.5)(cos60)(3)+V2’Cos(x)(0.5) V2’cos(x)= Perpendicular: M1V1+M2v2=M1V1’+M2V2’ 0=(0.5)(0.3)(sin60)+V2’sin(x)(0.5) V2’sin(x)= And the divide 2 by 1 Which is tan(x)=2/1 And then plug then back in to solve, but I don’t think we do it like this because...
4. ### I Question about transfer of Energy and Momentum in Ballistics

My apologies if the prefix is too high of complexity. I don't know where this would fall, difficulty or academically speaking. While it may be surprising to some given Hollywood's portrayal of it in movies, if a person in wearing hard bulletproof armor is struck by a projectile, the person is...
5. ### I Momentum, impact force and Earth

Suppose two objects, A and B, with large lengths LA and LB, and masses MA and MB, collide at time t0. Both objects before collision are vertical and aligned concentrically, being object B positioned initially at a higher z coordinate than object A. The bottom end of object A is rigidly...

7. ### Trouble with a Rocket Propulsion question (Variable Mass & Momentum)

I chose to set the upwards direction to be positive and dM/dt = R = 190 kg/s, so I can solve the problem in variable form and plug in. With the only external force being gravity, this gives M(t) * dv/dt = -M(t) * g + v_rel * R where M(t) is the remaining mass of the rocket. Rearranging this...
8. ### I Why is momentum considered a vector and kinetic energy a scalar?

I'm not interested in the mathematical derivation, the mathematical derivation already is based on the assumption that momentum is a vector and kinetic energy is a scalar, thus it proves nothing. Specifically, what happens if we discuss scalarized momentum? What happens if we discuss vectorized...
9. ### The velocity of a movable block that is penetrated by an arrow

This problem is in a chapter on momentum in the book basic engineering mechanics explained. Help me Mario
10. ### Perfectly inelastic collision of two moving and rotating disks

two moving and rotating, uniformly weighted disks perfectly inelastic collide. The disks are rotating in opposite directions (see the diagram) At the moment of their collision, the angles between their velocity and the line connecting their centers are 45 degrees. The velocities are therefore in...
11. ### Why momentum of a ball bounced off a wall increases twice fold?

Question 2a: It is really hard for me to get my head around this. The solution of this question mentions the momentum of the ball after it rebounds is 12kgms. My attempt at this solution is as follows Before collision Momentum of ball= mv= 2x3= 6 kgms and momentum of wall= 0 Therefore Total...
12. ### 1D Elastic Collision between an Elephant and a Fly

1 = elephant 2 = fly So I am trying to find v'2 which is the final velocity of the fly. I have v1 the initial velocity of the elephant 2.1m/s. So I plug it into the equation and have v'2=(2m1/(m1+m2))*2.1m/s. We are not given the masses so I just know m1>m2 but I don't understand how that will...
13. ### Confused about which forces are external when Newton's Second Law is used

So I have a trolley of mass m that moves on a straight line. A sphere of mass m, is attached on the trolley with a light string of length a and it is left to oscillate. Just to give some idea of their positions: r_trolley = xi r_sphere = (x-asinθ)i - acosθj (θ is the angle between the string...

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15. ### I Determining Momentum from Wavefunction

The goal I am trying to achieve is to determine the momentum (2D) in a quantum system from the wavefunction values and the eigenergies. How would I go about this in a general manner? Any pointers to resources would be helpfull.

20. ### I Physics of exercising and forces felt

Let's imagine an ideal scenario where you're lifting your own weight in its entirety. Let's say a woman weighing 100 lbs. Suppose she's doing an idealized handstand and pushup from that position. So she's lifting 100 lbs. Let's say ideally all of the forces are on her arms only. Do these forces...
21. ### I Is the classical relation between energy and momentum valid in QM?

Here we are talking about non-relativistic quantum physics. So we all know kinetic energy T = E - V = \frac{1}{2}mv^2 in classical physics. Here V is the potential energy of the particle and E is the total energy. Now what I am seeing is that this exact same relation is being used in quantum...
22. ### A silly question (perhaps) - Conservation of momentum for a cannon firing a cannonball

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
23. ### What's the error in my solution (Freight car and hopper)

Textbook solution: ##v## is the instantaneous velocity, $$P(t)=(M+b t) v$$ Then $$impulse = \Delta P = (M+b t) v = \int^{t}_{0} F dt'$$ Thus $$v=\frac{F t}{(M + bt)}$$ What I did instead was: Let ##M## be the instantaneous mass, and ##M_0## be the initial mass, then $$M=M_{0} + b t$$...

36. ### Two masses collide with a spring -- Find the final positions/velocities

Let's say you have two masses on either side of a spring. Mass 1 is connected to the end of a spring. The spring itself has no mass. Mass 2 is free in space. So you have: [M1]-[spring] [M2] So it's more descriptive, I'll name the variables like you might in programming. Let's define...
37. ### 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 lenght i put A as the initial extension but i am getting a wrong ans...
38. ### Projectile-car system and momentum

I have done question 1. But I'm struggling with the other one. So since the only thing I know about the rocket is the mass and the velocity, I guess I have to use momentum to solve this problem. From the first question, I found out that the x-velocity of the projectile is ##v_x=5...
39. ### I Clebsch–Gordan coefficients: An Identity

Hi, everyone. I'm trying to get the next identity It is in the format <j1, j2; m1, m2 |j, m>. I hope you can help me
40. ### I can't comprehend impulse = momentum

Here is my calculation: F = ma 50N = 1050kg * a a = 0.0476m/s² S = ut + ½at ² 1000m = 0t + ½(0.0476)t² t = 204.980s y = 204.980s (time to travel 1000m) since impulse = momentum, F * t = mv F * x = m * distance covered/y 50N * x = 1050kg * 1000m/204.980s 50N * x = 5122.450N⋅s x = 102.440s...

42. ### Physics momentum problem -- Collision between 2 blocks that stick together

So far I found the answer for a and b, but when I attempted to do the other ones I was completely lost. A.) P= MV M = 25g = .025kg V = 18 .025 * 18 = .45kg*m/s B.) KE= 1/2 mv^2 1/2 (.025)(18)^2 4.05 J
43. ### Bullet penetrating a block

Change in KE = Change in thermal energy 0.5 * (6)* vblock^2 = 0.4 * 6 * 9.81* 0.1 vblock = 0.885 By Conservation of Momentum, (0.05)(854) = (0.05)*vbu + (6)(0.885) I am not sure whether Change in KE = Change in thermal energy is true coz there should be a change in internal energy of the...
44. ### I Heisenberg Uncertainty: simple explanation required please

why can't we know where electron goes after it was hit by light? Light has a travel direction, can't we assume that electron bounces to the same direction that the light was headed??
45. ### I To which particles does ##p=mc## apply?

In A.P. French's Special Relativity, the author said the following, As I understand, photons are massless, so I don't think the last equation above applies to photons, but then, when deriving it, he used an equation proper to photons (##E=pc##). So in which context is ##m=p/c## valid?
46. ### 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 =...
47. ### 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!!!
48. ### Pushing a stalled car out of an intersection

Hints given: -Start with free body diagram. Use the relationship between impulse and momentum to find the final velocity of the car after he has pushed for time t. -Use a kinematic equation to relate the final velocity and time to the distance traveled. -What is his initial velocity? My...
49. ### Collision of a puck and a brick

x(before) y(before) x(after) y(after) puck (0.36)(13.8)=4.968 0 (0.36)(10.41)cos(α) (0.36)(10.41)sin(α) brick 0 0 (1.35)(1.34)cos(β) -(1.35)(1.34)sin(β) total 4.968 N*s 0 4.968 N*s 0 thus: (0.36)(10.41)sin(α) =(1.35)(1.34)sin(β) β= sin^(-1)[3.747sin(α)/1.809]= sin^(-1)[2.071sin(α)]...
50. ### Particle bouncing between walls

I thought it would be a good idea to pretend that the walls are stationary and that each time the particle hits a wall, it gets a velocity addition of the velocity of the wall it’s hitting. Using this I ended up at the formula V = initial velocity of particle + n(velocity of left wall) +...