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.
Homework Statement
A door ( a rod of length ##L##, mass ##M##) rotates with angular velocity ##\omega## about a point ## H ##, and approaches a stop at ##S##. ##H## and ##S## are along the same line, and separated by a distance ## s ##. Show that the angular momentum of the door about the point...
Homework Statement
If the steel disk has mass of 200 kg and a radius of 2 meters you can make it spin by applying a force to the rim. This torque increases the angular momentum of the disk. Suppose the force is 20 Newtons. How long would you have to apply it to get the wheel spinning 5...
Does the momentum always get transferred from lower velocity to higher velocity(may be along a negative velocity gradient.)
Consider the collision between 2 bodies M1 and M2,(M1<M2) but both having the same momentum.So M1 will have a higher velocity than M2(V1>V2). Now if the velocities V1 and...
Homework Statement
Prove that if a particle starts in a momentum eigenstate it will remain forever in a eigenstate given the potential c*y where c is a constant and y is a spatial variable.
Homework Equations
(h/i)d/dx is the momentum operator and a momentum eigenstate when put in the...
I have two balls spinning with v1, omega1 and v2, omega2. They collide elastically with no tangential slip, resulting in new values for v1, omega1 and v2, omega2. I have the two components v1 & v2 figured out in the plane of contact, where angular momentum does not come into play. But I am still...
< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >
My question is from an exam in analytic mechanics. The question was about an object sliding on inclined plane, the plane's angle is constant, and the plane is free to move along X axis. No...
Is the wavefront velocity if an OAM mode 1 light beam proportional to its wavelength?
I understand that the helical structure step length gives the wavelength of the beam. In this case, a small wavelength beam would travel much slower. The problem is, f=v/λ, but now v<c and if λ is shorter then...
I'm trtying to get a better understanding of the spatial part of the energy-momentum tensor, and although similar questions have been asked here, I think the point I do not fully grasp has not been covered so far.
The stress tensor can be considered as "momentum flux density" tensor.
If I...
Homework Statement
Spacecraft, with vacuum inside, in free-fall, contains a small mass captured against a fully-compressed compression spring against one wall of the craft. Release the spring and mass. Mass is accelerated by recovering spring (elastic potential energy turning to kinetic)...
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...
Good afternoon! I would like to preface by saying, yes, this is for a project. I am only posting here to see if my method of solving is correct before I finish the project incorrectly.
Homework Statement
I chose two balls, mass A: .553 kg and mass B: .410 kg
I recorded their collision and...
It is known that particles with rest mass cannot travel at the speed of light.
Can we also say that particles that travel at subliminal velocity, like these OAM photons do, have mass?
It has been demonstrated [1] that these beams can be thought as made of photons that posses intrinsic OAM, and...
Homework Statement
Homework EquationsThe Attempt at a Solution
I'm not sure how to go about working on this. What I have tried is this line of reasoning:
1x4He needs 2x3He. 2x3He needs 2x(2H + p)
Energy released is therefore 12.98 + 2(5.51) _+ 2(0.41) = 24.82 MeV.
However, it does seem...
Homework Statement
A punter drops a ball from rest vertically 1 meter down onto his foot. The ball leaves the foot with a speed of 18m/s at an angle of 55##^{\circ}## above the horizontal. What is the impulse delivered by the foot (magnitude and direction)?[/B]Homework Equations...
Homework Statement
Homework Equations
Momentum conservation and Energy conservation equations
The Attempt at a Solution
Ok First I translated the units, ##1000 \frac {kg} {min}=16.66\frac {kg} {s}##
##10\frac {km}...
I was watching a lecture and there was a connection drawn between classical rotational energy and quantum rotational excitation. The energy of a rotating system is $$E = (L^2) / 2 I $$ with L being the angular momentum and I the moment of Inertia. Then to make it quantum$$ n^2 * ħ^2$$ was...
Homework Statement
I was recently assigned a project of, tl;dr, building a wall to reduce the maximum force during a collision. Let me start by describing the setup as best as I can. First, here's an image:
These aren't the exact track and carts we're using, but they provide a great...
Homework Statement
A charged π meson (rest mass = 273me) decays into a neutrino (zero rest mass) and a μ meson (rest mass = 207me). Find the kinetic energies of the neutrino and the mu meson.
Homework Equations
E = moγc2
K = mo(γ-1)c2
v = pc2/E
p = moγv
The Attempt at a Solution
In the rest...
I know that in observable universe energy is not conserved.I don't know exactly why (it s possibly about GR and expanding universe but I don't know the equations)
In the observable universe...If we take a whole system like entire Observable universe, In this system is momentum conserved ...
I am studying Lineer Momentum.And I am not quite sure the understand the priniciples and basics of it.Is there any lecture video or note that I can understand better.Level should be undergrad freshman.
I am studying momentum and I just want to check that I understand the idea correctly.
Think there's a system.In this system there's two masses ##m_1## and ##m_2## moving with some velocity ##\vec v_1## and ##\vec v_2## and they exert a forces each other.Lets call the total force acting on...
Homework Statement
A proton has a speed of 0.2c. Find the speed of an electron that has (a) the same kinetic energy as the proton, and (b) the same momentum as the proton.
Homework Equations
K=ϒmc^2-mc^2
The Attempt at a Solution
This is what I did for the same kinetic energy part, but I...
Homework Statement
There is a man walking on a disk with mass 70 kg and speed 4 m/s. He walks on a circle with radius 1,5 m. How fast does the disk (mass 200 kg and radius 2 m) under him rotates (need to calculate angular velocity)[/B]
Homework Equations
angular momentum = J * w (J-moment...
1. Homework Statement
A small mass m slides without friction on a surface making a quarter-‐circle with radius R, as shown. Then it lands on the top surface of a cart, mass M, that slides without friction on a horizontal surface. (In practice, this cart could be a slider on an air-‐track.)...
How would ##[p_x, r]## be expanded? Where ##r=(x,y,z)##, the position operators. Do you do the commutators of ##p_x## with ##x, y,z## individually? So ##[p_x,x]+[p_x,y]+[p_x,z]## for example?
Homework Statement
I am happy to re-write the question, but I'm just leisurely working through a list of problems I found online, so here is the link (with picture).
http://web.mit.edu/2.25/www/5_pdf/5_01.pdf
Homework Equations
Cons of Momentum
Cons of Mass
The Attempt at a Solution
a) I...
Hi there.
So I had this lab last week about De Broglie hypothesis. In a simulation, we plugged in the electron velocity and the computer gave back a beautiful wavefunction, from which I can measure the wavelength. So here I have an electron going at 0.6 m/s with a wavelenght of 0.00060606...
Homework Statement
So, I'm doing this problem from Townsend's QM book
6.2[/B]
Show that <p|\hat{x}|\psi> = i\hbar
\frac{\partial}{\partial p}<p|\psi>
Homework Equations
|\psi(p)> = \int_\infty^{-\infty} dp |p><p|\psi>
The Attempt at a Solution
So,
<p|\hat{x}|\psi>
= <p|\hat{x}...
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)...
Homework Statement
A 2.9-kg particle P is located at [(r)\vec] = 3.3 m [^(x)] + 1.8 m [^(y)] from the origin of the x-y coordinate system shown in the Figure. It moves with a velocity of [(v)\vec] = −4.1 m/s [^(x)] + 2.6 m/s [^(y)]. A force, [(F)\vec] = 2.7 N [^(x)] + 1.4 N [^(y)] acts on the...
1. In the figure shown , a ball of mass m collides perpendicularly on a smooth stationary wedge of mass M , kept on a smooth horizontal plane. If the coefficient of restitution is e , then determine the velocity of the wedge after collision.
https://postimage.org/][/PLAIN]
Given
mass of ball...
I have a ball and the wind blows on it. Could I find the initial velocity of the ball from conservation of momentum?
m_air * v_air = m_ball * v_ball
v_ball = (m_air * v_air) / m_ball
What would you put for m_air?
Homework Statement
A muon has a mass of 106MeV/c2. Calculate the speed, momentum and total energy of a 200MeV muon(a muon with a kinetic energy of 200MeV).
Homework Equations
E=γmc
K+mc2=E
γ=1/(1-β)1/2
β=(v/c)2
The Attempt at a Solution
To solve for the speed I plugged E=γmc into K+mc2=E to...
This first question of mine is about momentum?
And opposite forses.
Lets think we have two batteries or something similar
spinning in space like in carusel structure.
And the batteries are athe more spinning end.
First the batteries are empty and we start loading
the first battery.
So em i...
I am working on a mechanism which controls the release of energy while remaining energy efficient. An image of the concept is shown below. (The image is meant simply to get an idea of how it would work- it is by no means perfect).
A source of energy (from a spring being released, for example)...
Homework Statement
A uniform solid sphere of radius R, rolling without sliding on a horizontal surface with an angular velocity ωo, meets a rough inclined plane of inclination θ=60°. The sphere starts pure rolling up the plane with an angular velocity ω. Find the value of ω.
Homework...
Hello.
Let's have two electrons with same orbital quantum number li and these electrons are in antiparallel; one electron has magnetic quantum number mi = a and and other electron has mi = -a (but we don't know which one has ml = a as we're in coupled representation to talk about total angular...
I can see how it would be conserved for the situation of a star turning into a white dwarf since the object is just contracting. Just like the classic ice skater example.
But what about a super nova? Say a star with spin up goes supernova and that the remaining black hole also has spin up but...
Hi everybody !
Can anyone help me with this problem:
Which is the (indefinite) integral with respect to time of the momentum of a particle of rest mass ##m_0##?
##\int \dfrac{m_0\;\mathbf{v}}{{\sqrt{1-\dfrac{\mathbf{v}\cdot\mathbf{v}}{c^2}}}}\;dt##
where ##m_0## is invariant with respect to...
Homework Statement
A rocket is fired from from the ground at initial velocity of ##v_0## and at an angle ##\theta##. At its highest height it splits into 2 parts of equal masses. The first part is fired straight up and at velocity ##v_0/2##. Find the angle and intensity of the second part...
To radiate energy, the Poynting vector must not drop faster than with the inverse square of the distance. Under what circumstances can EM angular momentum be emitted to the vacuum of space (i.e. without being recovered via inductive coupling) and yet not lead to energy losses through radiation...
Homework Statement
A stationary, axisymmetric, spacetime has two Killing vector fields [ξt, ξφ] corresponding to translation along t or φ directions. A particle of unit mass moving in this spacetime has a four-velocity u = γ[ξt + Ωξφ].
(i) Explain why we can interpret this as a particle moving...
Homework Statement
Magnetic puck A, with a mass of 0.100 kg, is pushed towards stationary 0.050 kg
magnetic puck B, to cause a head-on collision. You may neglect friction. The initial
velocity of puck A is 12 m/s [E]. Puck B moves with a velocity of 14 m/s [E], after
the collision.
a) Find...
Homework Statement
Homework Equations
I= sum m r2
L= r p
or
L=I W
The Attempt at a Solution
I= m1 r12 + m2 r22
I= 5.20 (0.9)2+ 2.20(0.9)2= 5.994 kg.m2
Then I used the second equation of second momentum
L(Angular momentum) = I W
L= 5.994 x 4.60
In the solutions sheet, he used the first...
Homework Statement
(This is a problem I myself created, so it may sound a bit trivial/stupid.) A particle of mass m in the xy plane has velocity v and a radius vector r with respect to some origin. After some time Δt, the same particle has velocity v and a radius vector r' with respect to the...
I wonder what would the angular momentum vector look like for these gears.
As it rotates, there is no clear direction on where the angular momentum vector is pointing. This object is symmetric.
Here's the video about these.
I often hear that a superconductor can hold a current indefinitely, I have a thought experiment which relates to this claim. Consider a closed square loop of superconducting wire, this wire carries some current. Will the electrons in the circuit transfer momentum and energy to the metal lattice...
We see in our solar system the planets orbiting the sun, but why doesn't with all of the other forces in play the perpendicular velocity seemingly not decrease(or does it?). And if the perpendicular velocity of the planets slow down would that result in static planets not moving around the sun?
Homework Statement
A 4 g bullet traveling at 500 m/s strikes a disk of mass 1 kg and
radius 10 cm that is free to rotate around an axis passing through its
center. The bullet’s incoming path is 5 cm above the rotation axis and
the bullet comes to rest in the position shown in the figure. At how...
Homework Statement
An m = 1.3 kg block and an M = 3.0 kg block have a spring compressed between them and rest on a frictionless table. With a stopper in place that prevents m from moving, the spring is compressed and released so that M moves away with a speed 2.0 m/s.
The spring is...