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.
Problem Statement: Are this 3 topics comes under laws of conservation of momentum?
Relevant Equations: Are this 3 topics comes under laws of conservation of momentum?
Are this 3 topics comes under laws of conservation of momentum: energy lost due to impact, inelastic impact, purely elastic...
Suppose that we have two balls (1) and (2) with the masses m1 and m2 and velocities v1 and v2, respectively. Furthermore, suppose that their momentums and kinetic energies are not the same so that P1>P2 and K1<K2. Which ball is more dangerous in hitting a person.
I calculated force vector by differentiating momentum vector.Since acceleration and velocity vectors are at45°,therefore force and momentum vector are at 45°.But i am not able to find the time at which it will take place.I tried F vector.P vector=FPcos45° but i am not getting from it.I also used...
Considering pilot wave interpretation, a singular particle measurements are fully defined (?) by knowing its wave function (a pilot wave) and the position of the "particle" (some hypotetical point particle riding on the wave). This should provide some sort of "realistic" explanation of how a...
I've come up with the following causes:
- air resistance
- parallax
- during the collision, some of the kinetic energy gets converted into thermal energy.
- invisible deformations
But I'm not sure which would be the biggest effect on the total momentum change.
Are there any other reasons that...
3. Find the hamilton equations
4. using 3. prove the the angular momentum in the z axis ##L_z=m(x\dot y-xy\dot)## is preserved.
I got in ##3##:
How can I prove 4?
Okay so I begin first by mentioning the length of the well to be L, with upper bound, L/2 and lower bound, -L/2 and the conjugate u* = Aexp{-iz}
First I begin by writing out the expectation formula:
## \langle p \rangle = \int_{\frac{L}{2}}^{ \frac{L}{2} } Aexp(-iu) -i \hbar \frac{ \partial }{...
I tried out the F=Δp/Δt equation and i came up with a change of momentum of the box-bullet fusion (M+m)V-0, but the textbook says otherwise (using a change of momentum of JUST the box itself, excluding the bullet). According to the textbook, the correct change is MV-0, without the added mass of...
What I know is the following:
The total angular momentum of the nucleus is just the total sum of the angular momentum of each nucleon.
If the nucleons are even the total angular momentum in the ground state will simply be ##0+##.
If the odd number of nucleons is close to one of the magic...
Although I've read many papers that propose a relation between action and entropy, I've been told that there is no generally accepted relation in physics.
But how/why are these concepts unrelated?
What about nobel laureate Frank Wilczek? He proposes that entropy and action are closely related...
Hi! I am trying to change the hydrogen ground state wave funcion from position to momentum space, so i solved the integral
Ψ(p)=(2πħ)^(-3/2) (πa^3)^(-1/2)∫∫∫e^(prcosθ/ħ) e^(-r/a) senθ r^2 dΦdθdr
and got 4πħ(2πħ)^(-3/2) p^(-1) (πa^3)^(-1/2) I am [(ip/ħ-1/a)^(-2)], which according to the...
I managed to solve the exercise, but I'm not sure if it's correct or not. I came up with this: p1+p2=P then p1+p2=0 then p1=-p2 and therefore i solved for p1 so that i could find p2, which is the NEGATIVE value of p1, according to the previous equation. I'm just concerned about this because...
A cyclist coasts along a road, he drives across a small puddle of water, after which the wheels leave wet lines on the road.
Now we concentrate our attention to the linear momentum of the water on a wheel. It decreases. Momentum is conserved, so what got the momentum that the water had?
Part (iii) is the part I am stuck on and is a 5 mark question. I have some idea of how to attempt it shown below
momentum is conserved so mux = mvy + mvz
(where ux is the initial velocity before the collision of ball x, vy is the velocity after the collision of ball y and vz is the velocity...
I was wondering why in the video the moment of inertia for the clay ball (upon collision) was simply 1ml^2. That is the constant for a hollow cylinder. The problem specifies that the object is a ball, so the cylinder classification makes no sense, and also I'm pretty sure clay is rather dense...
The fig. 1.1(a) is a mass m attached to a spring that is fixed to a wall. I don't understand what does "a sudden momentum impulse" means. Is it an external force o what?
I imagined that the new equation of motion would be
md^2x/dt^2+dp1/dt-kx=0
md^2x/dt^2+mdv1/dt-kx=0
is this the equation i...
So, I was reading my textbook in the section regarding net torque, and they gave an example of a seesaw with one person at each end, and they said that there is a net external torque due to the force of gravity on each person. I completely understand that; however, when I was reading another...
Okay so the first thing I did was was find the height of the apex. I found this by finding the x and y components of Vo:
Vox = VoCos(θ) = 22cos(59) = 11.33 m/s
Voy = VoSin(θ) = 22sin(59) = 18.86 m/s
Using the initial velocity of the y component I found the time it took to reach the apex:
t =...
Is there a relationship between the momentum operator matrix elements and the following:
<φ|dH/dkx|ψ>
where kx is the Bloch wave number
such that if I have the latter calculated for the x direction as a matrix, I can get the momentum operator matrix elements from it?
If an object is moving it has momentum .. but if the frame of reference is altered so the speed matches, the momentum apparently vanishes (?!). Likewise with apparent inertia during acceleration of an object - similar acceleration of the frame can radically alter the perceived affect. Can...
If i were to take one point as my origin and draw the two momentum, one for the initial collestion and one going from the wall after, from the origin point, then drawing horizontally i would get the answer as B as the resultant? Should i assume that for any resultant vector the direction can...
I had a question about the equation (1/2)mv^2...
Why is the velocity squared? Why not simply (1/2)mv? Does it have anything to do with the intrinsic angular momentum ie does the intrinsic angular momentum change in anyway as velocity increases in a particular reference frame leading to the...
So if we define point 1 at the entrance and point 2 at the exit, then we can write out Bernoulli's equation along a horizontal streamline as such: p_1 + \frac{1}{2}\rho v_{1}^2 = p_2 + \frac{1}{2}\rho v_{2}^2 = p_{atm}
One question is: won't there be p_atm also contributing to the static...
For this question, this is my working. The main issue is I cannot figure out where the factor of \frac{1}{2} comes from.
So I consider a control volume right around the propeller (in the frame of reference of the propeller) and I apply R(-->) Force = Change in Momentum Flux
F = \dot{m_{o}}...
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...
I don't have too much of a clue of how to begin the problem.
I first wrote the angular moementum of the system of particles: →M=∑mi(→ri×→vi)M→=∑mi(r→i×v→i). Then I know that the angular momentum from of the moving reference frame would have the velocity as the sum of the velocity of the frame...
Hello! Can someone point me to some table or functional form of the distribution of proton momentum inside deuterium? I found it for some high A (even for A=3), but can't find it for deuterium. Thank you!
n is the principal quantum number.
l is the angular momentum quantum number.
ml is the magnetic quantum number.
The possible values of l are 2, 3, and 4. I'm not sure if l can be equal to 4.
On the answer key, it shows l = 2, 3.
Hello,
I am an undergrad and am in an introductory level astrophysics course. I have a bit of confusion that I didn't know where to get help from so I made an account here. Please let me know if I miss some common etiquette or something... I don't understand how the slingshot maneuver...
My personal course of study in quantum mechanics hasn't brought me this far and so this question may be incredibly naive, but it has still been troubling me. If the energy of a photon is
E = (hbar)(omega)
and the units of hbar are J*s (obviously), then how can a photon have no mass if a J is...
1)In the first case the mass changes, in this manner:
m1= m1i - k Δt
impulse-momentum theorem:
F1Δt=Δq
FΔt=m1V1-m1iV1i
I now can replace m1 with its definition and obtain:
F1Δt= (m1i - k Δt)V1 -m1iV1i = m1iV1i - kΔtV1- m1iV1i = - kΔtV1
It is possible to remove Δt as it appears in both...
That said, my approach was to determine the energies and 3-momenta at the center of momentum reference frame for each particle, with a fixed s, and check it corresponds to each one of the above, but I'm having some trouble proving that, for example, E_A=\frac{s+m^2_A-m^2_B}{2\sqrt{s}}. I've...
Homework Statement
From Griffiths GM 3rd p.266
Consider a free particle of mass ##m##. Show that the position and momentum operators in the Heisenberg picture are given by$$ {\hat x}_H \left( t \right) ={\hat x}_H \left( 0 \right) + \frac { {\hat p}_H \left( 0 \right) t} m $$ $$ {\hat p}_H...
When do we use L=r x P and L=I x Omega (angular velocity)?
in old 8.01x - Lect 24, I pasted here link of the lecture, which will take you at exact time (at 27:02)he says "spin angular momentum" in classical physics lecture and why? I expected to hear "angular momentum" vector.
Normally...
In https://www.sciencedirect.com/science/article/pii/S0378437109010401, the author claims that the interference pattern obtained in the double-slit experiment does not need a wave description of matter, and can be accounted for by the "quantized momentum transfer" from the slits to the electron...
Homework Statement
A particle with mass M and speed v along the positive x-axis hits a stationary mass m. Two particles, each with mass µ, emerge from the collision, at angles with respect to the x-axis.
(a) Write the equation for conservation of the 4-momenta, for arbitrary angles θ_1, θ_2 of...
Hi,
once again I'm probably asking a question that is more about human physiology than physics (I recently asked a question that had to do with hearing).
I found a (definitely too hasty) reference to a ballistocardiograph in a high school textbook.
So I got curious about the way this apparatus...
I have a problem in mechanics.
On the wedge and block only the gravisational force (mg) is exerted (and there is no friction in this system).
What is asked in the question is the final velocities of the wedge and the block (vB, vK). The velocity of the block is conserved when it reaches at the...
I'm interested in knowing the ratio of momentum for a neutrino vs. a photon when both have the same energy. Alternatively, my spaceship engine can release 1GW of either a photon beam or a neutrino beam. How much relative thrust will the neutrino beam give me for the same energy (and power) as...
1. A system consists of a disk rotating on a frictionless axle and a piece of clay moving toward it as shown above. Outside edge of the disk is moving at a linear speed of V and the clay is moving at speed v/2. How does angular momentum of system after the clay sticks compare to the angular...
Given the figure, how can i arrive to this formula knowing that angular momentum is conserved?
I know that p = mv and L = p x r. So the initial momentum will be L1 = mV x R and the final momentum will be L2 = mv x r.
I am not sure how R will equal to b since the distance between the...
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...
I understand that in a system composed of two articles, the total angular momentum is:
J = J1 + J2
From the operators: J^2, Jz, J1z, J2z,J^21z,J^22z,
I get two possible sets of operators that commute:
{J^2, Jz, J^21z, J^22z} and {J^21z, J^22z, J1z, J2z}
What I don't understand is why the...
Hello forum.
I have a HW question that I don't fully grasp just yet. It was multiple choice and somehow I guessed the right answer based on the work I did complete, but I want to know how to get to the solution and which steps I'm leaving out. I'll follow the format to write out the...
Homework Statement
Two ice skaters have masses m1 and m2 and are initially stationary. Their skates are identical. They push against one another, as in Figure 7.11, and move in opposite directions with different speeds. While they are pushing against each other, any kinetic frictional forces...
Homework Statement
A fireworks rocket is moving at a speed of 45.0 m/s. The rocket suddenly breaks into two pieces of equal mass, which fly off with velocities v1 and v2. What are the magnitudes of v1 and v2?
Homework Equations
Conservation of Momentum
m1v1 + m2v2 = m1vo1 + m2vo2
The...
English isn't my main language, so I apologize in advance if something is unclear.
We are leaving air resistance out of this problem!
1. Homework Statement
We are going to describe the force F from the trampoline on the Joe as F = kx, k is a spring constant. This is a model.
1. Joe drops...