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.
In this question, the particles are constantly transmitting their momentum to the rocket. The force required to keep the rocket stable can be express as ##\vec F=(\vec v-\vec u)\dot m##.
However, when I tried to solve this question using the Newton's 2nd law, I found that the infinitesimal...
Hi,
I was trying to derive relativistic momentum equation using classical momentum equation but it didn't work. Could you please help me? Thank you!
Where am I wrong? Or, is not possible, in any way, to derive relativistic momentum using Newtonian momentum equation? Thanks!
So, what I did was suppose the mass of ramp is $ M_r$ and let velocity at B of block be v, then, after inellastic collsion both bodies v' velocity
at B ,
$$M\vec{v}= M_r \vec{v'}+ M \vec{v'}$$
or,
$$ \frac{M}{M +M_r} \vec{v}= \vec{v'}$$
Now,
Suppose I take the limit as mass of ramp goes to...
I was first wondering wether we can solve this question by applying conservation or energy or not but after googling it I found that we can't apply conservation of energy since there will be some energy lost in this case. I don't know how this energy is getting lost.
My second doubt was if we...
We know that photons (light) are massless but they have momentum. Now suppose I am in the space far away from planets/stars that there is no external force exerts on me, if:
1- I turn on a flashlight (torch), would I be pushed in the opposite direction which the flashlight is facing (Newton's...
Summary:: Would energy method give us a different answer from conservation of angular momentum?
Hello,
I do not know how to type equations here. So, I typed my question in Word and attached it here. Please see photos.
Note: This question is not a homework. I did not find it in textbooks or...
I was wathcing a video about radial velocity method for seeking exoplanet(video) and on 3:05 author writes that momentum of a star equal momentum of a planet. Why?
For the region where V = 0, solving the schrodinger equation leads to the above value of wave function, psi = sqrt(2/L) sin(pi x/L)
Since in the qus. it is not stated about the 'direction of movement' only restricted to +x direction, I think that the probability will be 1/2.
And finding the...
In which coordinate system the components of angular momentum are quantized? Better to say, if we can select the coordinate system arbitrarily, how the components of angular momentum, say z-component, are always ##L_z=m\hbar##?
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...
A gun is fired vertically into a block of wood(unknown mass) at rest directly above it. If the bullet has a mass of 24.0g and a speed of 310 m/s, how high will the block rise into the air after the bullet becomes embedded in it?
I read the Wiki page
https://en.wikipedia.org/wiki/Electron_cyclotron_resonance
as well as this answer here
How does a cyclotron work?
and it describes a setup where one has a cyclotron which has a static magnetic field pointing up through the dees and there is an alternating high voltage...
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 length i put A as the initial extension but i am getting a wrong ans...
Summary:: Griffiths problem 8.5
Problem 8.5 of Griffiths (in attachment)
I already solved part (a), and found the momentum in the fields to be $$\textbf{p}=Ad\mu_0 \sigma^2 v \hat{\textbf{y}}$$
In part (b), I am asked to find the total impulse imparted on the plates if the top plate starts...
Pretty much in a nutshell... fielded a question about how spin affects electron positron annihilation... ie do the spins have to be opposite in order to conserve angular momentum for two-photon annihilation to happen?
Intuitively I figured that looks reasonable ... but decided to check, and...
So as we know momentum has a formula p=mv right ?
But why we can't write it as p=m+v ?
The real question is why we multiply both mass and velocity quantity
And not add them ?
$$p=\gamma m v$$
$$F = \frac {md (\gamma v}{dt}$$
$$\int{F dt} = \int{md (\gamma v}$$
$$F t= \gamma mv$$
At this step, I don't know how to make v as explicit function of t, since gamma is a function of v too. Thankss
I first tried to get the solution by conserving the rotational kinetic energy and got ##\omega'=\frac2{\sqrt5} \omega##.
But, it was not the correct answer. Next I tried by conserving the angular momentum and got ##\omega'=\frac 45 \omega##, which is the correct answer.
Why is the rotational...
In an elastic collision, a 400-kg bumper car collides directly from behind with a second, identical bumper car that is traveling in the same direction. The initial speed of the leading bumper car is 5.60 m/s and that of the trailing car is 6.00 m/s. Assuming that the mass of the drivers is...
In this article it discusses the generation of something called super chiral light and claims with metamaterials they can make it have very high angular momentum like l=100. What does that really mean? How does that relate in magnitude to the normally computed linear momentum of a photon p=h/λ...
Summary:: this is what I've done so far... i don't think it works since i believe the information given is not even enough.
the formula I've used are
1. relativistic total energy = rest mass energy + kinetic energy (line 1, 3)
2. conservation of energy (line 4, 7, 8, 9)
3. conservation of...
How did you find PF?: Google
I know how to express Hamiltonian for scalar field written in field operators through the raising and lowering momentum operators, but I can't figure out how to do the same for the number of particles written in field operators: the 1/2E coefficient within the...
Hello,
I have this i am learning. I have been trying to find information online but have struggled to find anything which helps me. YouTube usually has good videos, but doesn't seem to on this. This is one topic i have never learned before. But keen to.
I was hoping someone could help me...
Linear Motion Equation to get the common velocity of the block and bullet just after collision:
v2=u2+2gs, I set v=0 at max height of s = 0.004 m and g = -9.81 m s-2
I got u = 0.28 m/s
Then I calculate the impulse of the block using formula J = mv - mu, where v=0 and u=0.28 m/s and I got J = 1.4...
IS my solution right? Comparing with the other solutions, the answer just exchange the signals, i don't know why,
THats what ifound.
And here is the three equations:
{i use the point which occurs the collision}
Lo = Lf >>
0 = Iw + M*Vcm(block)
Eg = ct>
mvo² = mvf² + MVcm² + Iw²
I = ml²/3...
The Schwarzschild metric seems to model, for example, the earth’s gravity field above the earth’s surface pretty well, even though the Earth is not really a golf-ball sized black hole down at the center. Can the same be said for the Kerr metric? Does it model a rotating extended body’s gravity...
Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds!
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I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...
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...
On p.170 of French's book on special relativity there is this thougth experiment attributed to Lewis and Tolman (1909). It is about two individuals throwing identical balls of mass M at each other with identical speed. The balls bounce against each other and are caught again.
See attached...
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...
I'm reading the article https://www.researchgate.net/publication/267938119_ON_THE_GALILEAN_COVARIANCE_OF_CLASSICAL_MECHANICS (pdf link here), in which the authors want to establish the transformation rule for momentum, assuming only that ##\vec{F}=d\vec{p}/dt## and notwithstanding the relation...
Since the equations are, actually, the question, i will post the image with relevant equations here:
it seems strange, I'm almost sure that I didn't make a mistake in the differentiation, but differentiating 9.8b I found 9.7a with both positive terms
To my mind because one particle has momentum ##\vec{p}## and the other one ##\vec{0}##. It is for instance necessary to find reference frame where one momentum will be for instance ##\frac{1}{2}\vec{p}## and the momentum of other particle should be ##-\frac{1}{2}\vec{p}##. So it is necessary to...
I believe momentum conservation is to be used in this sum since there's no external force, but I am not sure how to write the equation.
Can someone please help me out:)
Angular momentum can be exchanged between objects in a closed system, but total angular momentum before and after an exchange remains constant (is conserved).
There is a proof about this conservation?
"A smooth horizontal disc rotates with a constant angular velocity ω about a stationary vertical axis passing through its centre, the point O. At a moment t=0 a disc is set in motion from that point with velocity v0. Find the angular momentum M(t) of the disc relative to the point O in the...
given z(0) = 0 as well as
˙z(0)=0
How would one find the angular momentum along the x-axis in terms of t.
Currently, I have formulated the following:
$${\ddot{z} = \frac{g}{1+(\frac{4R}{s})^2}}$$
Hi
With the 2-body problem relating to planetary orbits i have encountered the following ; the gravitational force on the reduced mass acts towards the large mass(Sun) and since it is a central force it exerts no torque about the fixed centre(Sun) so angular momentum is conserved.
Conservation...
Well I am pretty sure that the kinetic energy stays the same because in this case the velocity vector and energy make a ninety degree angle so no work is done, but I am lost about angular momentum. It could decrease maybe if the torque is clockwise while the ship is going in a counterclockwise...
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