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
I'd like to show, if possible, that rotational invariance about some axis implies that angular momentum about that axis is conserved without using the Lagrangian formalism or Noether's theorem. The only proofs I have been able to find use a Lagrangian approach and I'm...
Homework Statement
What will momentum measurement of a particle whose wave - function is given by ## \psi = e^{i3x} + 2e^{ix} ## yield?
Sketch the probability distribution of finding the particle between x = 0 to x = 2π.
Homework Equations
The Attempt at a Solution
The eigenfunctions of...
Hi all, I have a few questions. Thanks in advance!
Phonons:
Can phonons be thought of as a quantised wave of sound, in the same manner photons being a quantised light wave? Also, can they be taken as particles of sound in the same way that photons can be particles of light?
Crystal momentum...
Hello! I got a bit confused about the fact that the whole the description of spin (and angular momentum) is done in the z direction. So, if we are told that a system of 2 particles is in a singlet state i.e. $$\frac{\uparrow \downarrow -\downarrow \uparrow }{2}$$ does this mean that measuring...
My intuition is if an object is orbiting a centre, it is accelerating as the direction of its vector constantly changes, i.e a ball orbiting a stick because they are tied by a string. I don't understand why Earth's spin does not slow down, if we think of Earth as lots of individual atoms, those...
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...
##\ \ \ \ \ ##Calculate the 4 momentum of a rotating rod. We divide it into 4 parts. The part 1 is the work of predecessors.
##\ \ \ \ \ ##In Special relativity, the motion of rod AB (which is an object in non inertial motion) can be described in an inertial reference frame and the motion of rod...
Homework Statement
So the problem is trying to isolate mA in the equation for momentum (only focusing on top formula, not bottom hehe) basically by solving the equation I assume. My teacher said because the vA and vB on the right were prime they could not be combined so I'm having trouble...
Homework Statement
Consider two pairs of operators Xα, Pα, with α=1,2, that satisfy the commutation relationships [Xα,Pβ]=ihδαβ,[Xα,Xβ]=0,[Pα,Pβ]=0. These are two copies of the canonical algebra of the phase space.
a) Define the operators $$a_\alpha =...
Homework Statement
How can we calculate the velocity at stack tip if the distance of larger diameter is 2.5 m?
I think i cannot use the equation of V1A1 = V2A2 because they may have some effect from 2.5 m of distance.
Thank you very much.
Homework Equations
Q1=Q2
The Attempt at a Solution...
Homework Statement
A certain odd-parity shell-model state can hold up to a maximum of 4 nucleons. What are its values of J and L? What about an odd-parity shell-model state with a maximum of 6 nucleons?
Homework Equations
Parity = (-1)L
J = L+S
Total angular momentum, J, is equal to orbital...
Problem goes: A rubber ball, traveling in a horizontal direction, strikes a vertical wall. It rebounds at right angles to the wall. The graph below illustrates the variation of the ball’s momentum p with time t when the ball is in contact with the wall.
Which of the following statements is...
Homework Statement
A particle of mass m moving with velocity v1 leaves a half-space in which its porential energy is a constant U1 and enters another in which its potential energy is a different constant U2.
Determine the change in the direction of motion of the particle.
Homework Equations...
Homework Statement
Mass m1 = 2kg traveling at v = 3 m/s
Mass m2 = 3kg traveling at v = 2 m/s
After an elastic collision (from opposite directions) what will be the momentum and velocities of each of the bodies ?
Homework Equations
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Momentum = mass x velocity
##K.E = \frac {1}{2}.m.v^2 ##...
From classical EM theory, we know that if we shine light of frequency ω on a second order non-linear medium, a radiation of frequency 2ω is created. The amplitude of the radiation of frequency 2ω is dependent on the momentum difference between the incident field and the created field. But I...
as we know light has momentum so theoretically we can use it but is it practical?
(also this is it that light only exerts force if incident on something?)
Homework Statement
Freight car and hopper*
An empty freight car of mass M starts from rest under an applied force F. At the same time, sand begins to run into the car at steady rate b from a hopper at rest along the track.
Find the speed when a mass of sand m has been transferred.Homework...
Hello. I'm currently entering into a Physics II class at the start of my third semester at UCONN (my first semester was introductory modern physics - kinetic theory, hard-sphere atoms, electricity and magnetism, scattering, special relativity, Bohr model, etc), and finished Physics I off with...
[Mentors' note: This thread's prefix has been set to 'B']
We all know that the quote in the title is an imprecise convenience when talking about the Heisenberg uncertainty principle in a context where we would not want to enter into conceptual or fundamental issues to make a more correct...
In a solution to a problem we were given, it is written that a positron momentum with energy of 2mc2
(where γ=2) is √(γ2-1)*mc = √(4-1)*mc = √3*mc
How did they get that P=√(γ2-1)*mc?
Homework Statement
A rod (mass M, length L) is placed vertically on a smooth horizontal surface. Rod is released and after some time velocity of COM is v downwards and at this moment rod makes 60 degrees with horizontal. Find angular momentum of rod about Instantaneous center of rotation...
Homework Statement
A circular ring (2m, R) with a small insect of mass m on its periphery, is placed upon smooth horizontal surface (axis of rotation passing through center and perpendicular to the ground i.e disk is lying horizontally)
. The insect starts moving with velocity v w.r.t ground...
Homework Statement
suppose you're sitting on a rotating stool holding a 2kg mass in each outstretched hand, if you suddenly drop the masses, will your angular velocity increase, decrease or remain the same?
Homework Equations
dL/dt=net torque
when net torque is 0, L=constant=Iw
therefore...
Homework Statement
Assertion- If linear momentum of particle is constant, then its angular momentum about any axis will also remain constant
Reason-Linear momentum remains constant when net force is 0, angular momentum remains constant when net torque is zero
which of these statements is/are...
Homework Statement
A uniform rod (M, L) is rotated about a point L/3 from its left end. Angular momentum about O
Homework Equations
1) L=I(cm)w for purely rotating body
2) L(orbital)= M*v(cm)*perpendicular distance(r)
3) L(spin)= I*w
The Attempt at a Solution
I got the correct answer in two...
Homework Statement
A disk is undergoing pure rolling motion with speed v. The radius of the disk being R and mass M. Then the angular momentum of the disk about the
1)bottom most and
2)top most point
Homework Equations
1) L(orbital) = m*v*r where v is the velocity of cm which is...
The process is known as counter-propagating Spontaneous Parametric Down-Conversion (CP-SPDC).
In regular SPDC, a photon from a (pump) laser enters a transparent nonlinear crystal at rest, and gets converted into a pair of photons whose total energy and momentum add up to that of the original...
Homework Statement
A block of mass m slides down a wedge of mass M and inclination theta from rest. All the surfaces are smooth. Find the speed of the wedge when the speed of the block w.r.t to wedge is v.
Homework Equations
V(c.m.)=m1v1+m2v2/(m1+m2)
The Attempt at a Solution
Conserving...
Homework Statement
A 7.3-cm-diameter baseball has mass of 150 g and is spinning at 230 rad/s .
Treating the baseball as a uniform solid sphere, what is its angular momentum?
I'm about to pull my hair out because I feel like I understand everything about this problem perfectly and yet I'm still...
In particle phyisics four-momentum is used and De Broglie relation is used to understand what lenghts can be "seen" in an experiment.
Here (page 6) https://people.phys.ethz.ch/~pheno/PPP/PPP2.pdf it is claimed
Where ##Q^2## is not actually "momentum" but its the square of the four momentum...
ok so 1- the magnetic momentum is = to u in the k axis ( xyz - ijk )
and the magnetic field B = -A/z4 + Be^Cz) , also in the k axis orientation
so the magnetic force F , that is applied on the magnetic momentum is given by
4 choices ; and as i can understnd it, 3 of them are...
Homework Statement
Calculate the momentum of a 140 eV photon.
Homework Equations
p = E/c
The Attempt at a Solution
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First, convert eV to Joules
140eV (1.60 x10-19J)
= 2.24 x10-17J
Now for momentum:
p = mv
p = (E/c2)v
p = E/c
In my course, however, it says for photons E = hc/ λ...
Homework Statement
Four particles of mass 1 Kg each, are moving on a plane with the velocities given in the figure.
Homework EquationsThe Attempt at a Solution
First I calculated the position of the CoM:
Xcm=7/4(i + j)
Then I calculated the velocity of the CoM:
Vcm= ½i + ¼j
For the internal...
I am a hobby reader/listener of pysics, astronomy, special relativity, black holes and more. And a question arose that no amount of YouTube has touched on.
Sorry if this is just a stupid question from a hobbist but it truly has me stumped. Or maybe I just have been taught by...
I found that the equation is expressed by
there is outer product ...what I really don't get it is if j is a vector then the outer product of j and j is is obtained by multiplying each element of j by the complex conjugate of each element of j which is basically a matrix not a vector
Hello,
in classical physics orbital angular momentum is defined as the cross product of the position vector 'r' and the momentum 'p'. A friend told me that all moving objects must have orbital angular momentum (even if it is moving along a straight line). That statement confuses me a lot...
I need to prove that in a vacuum, the energy-momentum tensor is divergenceless, i.e.
$$ \partial_{\mu} T^{\mu \nu} = 0$$
where
$$ T^{\mu \nu} = \frac{1}{\mu_{0}}\Big[F^{\alpha \mu} F^{\nu}_{\alpha} - \frac{1}{4}\eta^{\mu \nu}F^{\alpha \beta}F_{\alpha \beta}\Big]$$ Here ##F_{\alpha...
From a wiki's vis-viva equation page, it is given that the specific angular momentum h is also equal to the following:
h = wr^2 = ab * n
How can ab * n be derived to be equal to the angular momentum using elliptical orbit energy/momentum/other equations without having to use calculus or...
If a pulse of light, which has momentum p = E/c, interacts with particles of air, would it not change their momentum over time, causing mechanical energy (sound)?
As I understand it, sound is mechanical energy moving through particles as they vibrate. Why can't the momentum of a pulse of light...
I was solving an exercise from Cohen's textbook, but then I got stuck in this question.
"Let ψ(x,y,z) = ψ(r) the normalized wave function of a particle. Express in terms of ψ(r) the probability for:
b) a measurement of the component Px of the momentum, to yield a result included between p1...
In Special Relativity, we have the four vector, (E/c, px, py, pz). However, isn't the first term just `p` given that `E=pc` for a photon? Why is it an energy-momentum four vector when the first term isn't really energy but momentum?
Homework Statement
I have a lambda decaying into a pion and a proton. The lambda is moving with velocity 0.9c and I know the mass of the lambda as well as the pion and proton (these are known constants). I need to find the momentum of the pion and the proton after the decay happens.
Homework...
Homework Statement
There is a 4 kg mass that has a speed of 6 m/sec on a horizontal frictionless surface. The mass collides head-on and elastically with an identical 4 kg mass initially at rest.
The final speed of the first 4 kg mass is:
(a) 0 m/s (b) 2 m/s (c) 3 m/s (d) 6 m/s
Homework...
Hello Everyone. I Was Wondering how excatly the Gauge invariance of the trace of the Energy-momentum tensor in Yang-Mills theory connects with the trace of an Holonomy.
To be precise in what I'm asking:
The Yang-Mills Tensor is defined as:
$$F_{\mu \nu} (x) = \partial_{\mu} B_{\nu}(x)-...
Homework Statement
A particle A (mother particle) with a mass of mA decays to two particles B and C (daughter
particles) with mass values of respectively mB and mC. Calculate momentum of the two
daughter particles, pB and pC. (at first the mother particle is at rest)
Homework Equations
The...
Homework Statement
A particle with mass m is moving on the x-axis and is described by
## \psi_b = \sqrt{b} \cdot e^{-b |x|}##
Find the probability distribution for the particles momentum
Homework Equations
## \Phi (p)= \frac{1}{\sqrt{2 \pi}} \int_{-\infty}^\infty \Psi(x,0) \cdot e^{-ipx} dx##...
Homework Statement
A point charge q sits at the origin. A magnetic field ##\mathbf{B} (\mathbf{r})=B(x,y)\mathbf{\hat{z}}## fills all of space. The problem asks us to write down an expression for the total electromagnetic field angular momentum ##\bf{L_{EM}}##, in terms of q and the magnetic...