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 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...
It's really confusing if the frictional force IS an external force..
My guess is the frictional force isn't an external force
and therefore I can observe the momentum conservation even with friction if I carefully measure the velocity right before and after the collision.
But I'm not sure about it..
Homework Statement
A long board is free to slide on a sheet of frictionless ice. A skater skates to the board (laid horizontally relative to the skater's motion) and hops onto one end, causing the board to slide an rotate. In this situation, are angular and linear momentum conserved...
Homework Statement
How to determine variation of mean momentum of a nucleon with the mass number A of nucleus?
Homework Equations
R=R_0A^(1/3)
The Attempt at a Solution
Can't find a solution with elementary approach.
Homework Statement
Homework Equations
a = v/t
p=mv(?)
The Attempt at a Solution
If an engine is turned on, that means that the ships are accelerating since the engine pushes back on air with a force and air pushes back to propel the ships forward, so I thought (A) would be the answer, even...
In the Dirac equation, the wave-function is broken into four wave-functions in four entries in a column of a matrix. Since there are four separate versions of the wave-function, does each version have the spin angular momentum of h-bar/2? This seems overly simplistic. How does spin angular...
Hi, I found some back of envelop calculations which show that Jupiter accounts for over 60% of the solar system's angular momentum.
http://www.zipcon.net/~swhite/docs/astronomy/Angular_Momentum.html
Is that correct?
A previous thread here on the subject ( now locked for some reason ) claimed...
1. At the instant of the figure, a 6.70 kg particle P has a position vector of magnitude 4.30 m and angle θ1 = 43.0° and a velocity vector of magnitude 3.40 m/s and angle θ2 = 32.0°. Force , of magnitude 7.40 N and angle θ3 = 32.0° acts on P. All three vectors lie in the xy plane. About the...
Homework Statement
I am working on the derivation of Kepler's Second Law based on torque and angular momentum. I understand that the vector "L" is equal to the mass (m) times the cross product of the vector "r" and the vector "v." The source I am following then states that
L = mrvtheta. I do...
Homework Statement
We know the momentum of an electron, which is: 1,48*10^-21.
Momentum is m*v (mass*speed)
If we divide the momentum by the mass of the electron to find electron's speed, it'll give a value where v> 3*10^8 m/s.
Since speed can't be above speed of light, we have to calculate...
Homework Statement
the rate of change of the total momentum in a system with respect to time is zero.
thus, my textbook says, the total momentum of that system is constant.
i'd like to understand how one implies the other if anyone could give me a conceptual explanation? i understand the...
I just want to state that i DID solve the problem. I just seek understanding of it.
I'd be really grateful if someone could answer two of my questions at the end of this post. The problem I've solved here is just to show what I'm dealing with.
1. Homework Statement
Object 1 is moving towards...
(I hope this post doesn't cross the border into the forbidden realm of quackery and speculation.) I have what seems like a simple question about Special Relativity but I haven’t seen it discussed anywhere, nor has anyone I've asked.
Does the nonlinearity of the Lorentz factor provide a way...
Homework Statement
[/B]
Parts (c) and (f) are the ones I'm having trouble with;
Homework EquationsThe Attempt at a Solution
[/B]
For (c), I assume the problem is meant to involve using the result from part (b), which was H = g(J2 - L2 - S2)/2 .
I was trying just to do it by first showing...
Hi guys...i'm not able to understand the rate of change of angular momentum. Suppose i have a disk rotating with an angular velocity vector w along the axis, so the angular momentum is: L=(InertiaTensor)*w, now if i apply a torque the L will change according to...
Homework Statement
Homework Equations
Li = Lf
L = I*omega
K = (1/2)*(I)*(omega)^2
The Attempt at a Solution
[/B]
Given that there are no non-conservative forces in action, I am assuming that the two kinetic energies should be equal. However, as shown by my work above, the two values...
Homework Statement
If I want to find the difference in velocities of 2 objects A and B
We know the sum of their velocities is A + B
But but is the difference B - A
Why not A - B?
Homework Equations
This is from the equation of calculating restitution where
(greek letter) = (The difference in...
Homework Statement
A cylinder with radius ##R## and height ##h## which has a distributed charge on its surface with density ##\sigma## spins over its axis with angular velocity ##\omega##.
If the cylinder has a mass density ##\rho##, find the relationship between magnetic momentum and angular...
Homework Statement
Find magnitude of momentum of both blocks
Homework Equations
p=mv
The Attempt at a Solution
I am doing my homework right now and just need help understanding finding the total momentum given a before collision/ after collision situation. So i am unsure if i should take the...
Homework Statement
I've spent at least 1.5 hours on this problem trying to figure out what i did wrong and I can't find anything. With an exam in two days plus another chapter to go through.
Regardless, here are the problem(6) and answer, as well as my work. Hope you can read it, and the...
1. Homework Statement
in picture
Homework Equations
momentuma+momentumb=momentum of system
The Attempt at a Solution
So i just spent 1 hour trying to solve this problem and got completely stuck when trying to solve for the angle of ball 2 in the final position i ended up with an equation...
1. Homework Statement
In picture above
Homework Equations
impulse = Δp[/B]The Attempt at a Solution
4.28NS = Δp
4.28NS = pfinal - pinitial
4.28NS + 0.18kg*0.16m/s = pfinal
(4.28NS + 0.18kg*0.16m/s)/.18kg = vfinal
vfinal = 39.77777778m/s
Now i got the direction incorrect but the magnitude...
Homework Statement
m = 50kg
Distance covered = 100m
T = 3.22
Solve for average momentum.
Homework Equations
X = 1/2 at^2
p = mass*acc*change time
The Attempt at a Solution
100 = 1/2 a (3.22)^2
a = 200/10.3684 = 19.28937m/s^2
f = 50 * 19.28937 = 964.4689
change momentum = 964.4689 * 3.22 =...
I've learned that in a crystal, the crystal momentum is conserved. When one considers the electrons as Bloch waves, they have a momentum that doesn't commute with the Hamiltonian and they have well definite energies, hence they cannot have a well definite momentum, because there is no basis in...
Homework Statement
I have been asked to calculate the momentum of a photon in that has been ejected as a gamma ray after a nucleus was excited in terms of the Energy. I am confused as to whether or not I can use two different equations
Homework Equations
E=mc^2 or E=hf λ=h/p
The Attempt at a...
Homework Statement
There's a car, there's a cannon strapped on top of a car, the car travels with a velocity of 20 m/s and the cannon fires. The cannon fires a ball at 200 m/s. What is the velocity of the car? Velocities are with respect to the ground.
mass car = 1000
mass cannon = 100...
Homework Statement
Consider a rocket subject to a linear resistive force, $$f = -bv$$, but no other external forces. Use Equation (3.29) in Problem 3.11 to show that if the rocket starts from rest and ejects mass at a constant rate $$k = -\dot{m}$$, then its speed is given by:
$$v =...
Homework Statement
Homework EquationsThe Attempt at a Solution
Hi All,
My problem is that when I calculate this integral or use software to do it for me I get (3*i*pi)/16, when I've been told that the answer is 1/2i giving a probability of 1/4. Would someone be able to point out where my...
I explained this thinking to a meteorologist once and she couldn't give me an answer. Any physicists want to give it a shot?
I find the typical explanation of tornadoes perplexing (that's a polite way of saying I don't believe it). The explanations I've seen claim that tornadoes start out...
Homework Statement
Homework EquationsThe Attempt at a Solution
How do I calculate part d?
I know that (m2-m1)v0 = m2v2+m1v1
where v0 = root (2gh), v1 and v2 are the new velocity of the masses
(m2+m1)v02 = m2v22 + m1v12
I also know that v2-v1=2v0
but how do I separate the KE of mass 2?
Homework Statement
Given ##\hat{x} =i \hbar \partial_p##, find the position operator in the position space. Calculate ##\int_{-\infty}^{\infty} \phi^*(p) \hat{x} \phi(p) dp ## by expanding the momentum wave functions through Fourier transforms. Use ##\delta(z) = \int_{\infty}^{\infty}\exp(izy)...
Hello all,
I have a question regarding the precise definition of angular momentum in orbital motion.
I see one definition says angular momentum h, position, r, and radial velocity, r_dot, are related as follows:
h = r x r_dot.
However, I also see one definition that says h is related to r and...
Homework Statement
A 25kg child is spinning on a merry-go-round of mass 150kg and radius 2m at a constant angular velocity of 1rev/s. The child slowly walks to the center of the merry-go-round. Treat the child as a point mass and the merry-go-round as a uniform solid disk, and neglect friction...
I learned that the Poynting vector was the electromagnetic density of momentum but recently, while reading the Electromagnetic_stress–energy_tensor article at Wikipedia, I thought about the implications of the momentum conservation equation and arrived to an inconsistency, this equation is...
Homework Statement
Hi I'm having trouble with a question that's asking me to calculate the precession rate for a spinning top. The trouble that I'm having is that I don't understand how the angular momentum points along the axis of the spinning top (picture attached). When I use the formula...
In QM, the inverse distance operator ##\hat{r}^{-1}## appears often because of the association to Coulomb potential. The operator of inverse momentum, ##\frac{1}{\hat{p}}## is a lot more rare.
In the book "Exploring Quantum Mechanics: A Collection of 700+ Solved Problems for Students, Lecturers...
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...
Homework Statement
1. Two skateboarders start from rest on opposite sides of a ramp like the one in the image, roll down and collide elastically on the level part of the ramp. The masses of the skateboarders are m1 = 48 kg and m2 = 55 kg and they both start from the height h = 4.70m. Ignoring...
I recently found this article about the dynamics of the wave function. It has some good simple illustrations and I found it valuable. But the author has a question himself, about understanding the Schrodinger equation. I wonder if anybody here could fill in the missing piece. The relevant part...
Homework Statement
Homework Equations
because their is steady flow we only care about mass flow flux meaning
m1vout - m2vout
m = ##\rho##Av
i know that m1 = m2 + m3
since there are no dimensions I am assuming that areas are the same everywhere, density does not change therefore velocities...
Homework Statement
Hi,
I do not know how to resolve question 1d and 2d at all. I hope the rest is well resolved, not sure about 1c and 2c. Can someone check my work and help me resolve problem with this questions, please?
Task
A hammer of mass 1700kg is dropped 2.5m under its own in fluency of...
Homework Statement
Find the 2 unknown variables.[/B]Homework Equations
Am I doing this right? Can someone help me find the solution?[/B]
The Attempt at a Solution
To compute for the velocity of the target/arrow combination immediately after the collision:
M_bV_{bi}=M_bV_{bf}+M_wV_{wf}...
Homework Statement
On a frictionless, horizontal air table, puck A (with mass 0.250 kg ) is moving toward puck B (with mass 0.360 kg ), that is initially at rest. After the collision, puck A has a velocity of 0.125 m/s to the left, and puck B has velocity 0.655 m/s to the right.
I already...