In introductory mechanics, the momentum of a particle is its mass times its velocity. In electrodynamics, the momentum of a field is proportional to the cross-product of the electric field with the magnetic field. In special relativity, momentum is generalized to four-momentum.
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Derivative of a Position Eigenket
I was flicking through Zettili's book on quantum mechanics and came across a 'derivation' of the momentum operator in the position representation on page 126. The author derived that ...
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905 views
Conservation of Momentum/Energy collision Problem
I'm working on a physics problem in preparation for the MCAT and there's this particular problem that's troubling me. I don't know if it's a bad question or if I'm not understanding some sort of ...
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909 views
Momentum-Representations in Quantum Mechanics
Why do we get information about position and momentum when we go to different representations. Why is momentum, which was related to time derivative of position in classical physics, now in QM just a ...
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305 views
block slides on smooth triangular wedge kept on smooth floor.Find velocity of wedge when block reaches bottom
Find the velocity of the triangular block when the small block reaches the bottom:
Here is what I did:
The final velocity(at the bottom)of the small block of mass m is $\sqrt{2gh}$ along the plane ...
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4answers
386 views
Is the momentum operator well-defined in the basis of standing waves?
Suppose I want to describe an arbitrary state of a quantum particle in a box of side $L$. The relevant eigenmodes are those of standing waves, namely
$$ \left<x|n\right>=\sqrt{\frac{2}{L}}\cdot ...
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1answer
301 views
Momentum as Generator of Translations
I understand from some studies in mathematics, that the generator of translations is given by the operator $\frac{d}{dx}$.
Similarly, I know from quantum mechanics that the momentum operator is ...
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3answers
248 views
Conservation of Energy in Different Frames of Reference
Say I have a bucket of fuel that can produce 150J of energy by combustion. No matter what frame of reference an observer or the bucket of fuel is in, since the configuration of molecules stay the ...
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1answer
1k views
How do kinetic energy and linear momentum relate?
It took me quite a long time to click my gears in place and even then I'm not sure it's completely correct.
The problem is that I need to understand these concepts (physics concepts; not just these ...
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2answers
2k views
What is p_T? (transverse momentum?)
I've been looking at a few papers in experimental physics (from the ATLAS collaboration, for example) and I've often run across phrases such as "high-p_T electron." What exactly is p_T? Is it simply ...
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2answers
855 views
Quantum momentum (De Broglie)
The de broglie hypothesis suggests a particle can be associated with a wave of
momentum $p = \hbar k$
my question is the following: how does one arrive at this concept of the momentum of a wave?
I ...
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1answer
663 views
Confusion between the de Broglie wavelength of a particle and wave packets
So I learned that the de Broglie wavelength of a particle, lambda = h/p, where h is Planck's constant and p is the momentum of the particle. I also learned that a quantum mechanics description of a ...
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58 views
Two-body problem questions
I am self studying the two body problem and I'm stuck on the following:
I have given $$\ddot{\vec{x}}_1= - G m_2 \frac{\vec{x}_1-\vec{x}_2}{|\vec{x}_1-\vec{x}_2|^3}$$ and $$\ddot{\vec{x}}_2= - G ...
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72 views
Conservation of Linear Momentum at the point of collision
This is a pretty basic conceptual question about the conservation of linear momentum.
Consider an isolated system of 2 fixed-mass particles of masses $m_1$ and $m_2$ moving toward each other with ...
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3answers
190 views
Where do the conservation laws come from?
I know the conservation of energy comes from Noether's theorem via the time-translational symmetry, and if I remember correctly, the conservation of momentum comes from space-translational symmetry.
...
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1answer
477 views
Conservation of linear and angular momentum
Suppose I have two rigid bodies A and B and they are connected by a spring which is attached off-center (thus possibly causing torques). Due to the spring a force $f$ acts on A and a force $-f$ acts ...
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1answer
142 views
Why is momentum conserved when a ball hits a vertical wall?
Almost in every book on physics, there's an example of conservation of momentum when the ball that is moving horizontally in the air, hits some massive wall. They claim that the return speed of the ...
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1answer
368 views
Simple 2D Vehicle collision physics
I'm trying to create a simplified GTA 2 clone to learn. I'm onto vehicle collisions physics. The basic idea I would say is, To apply force F determined by vehicle A's position and velocity onto point ...
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4answers
737 views
Is it possible to lift yourself off from the ground?
Say for instance a person who was strong enough to lift double his body weight. If he placed his hands under his bottom and tried to lift$^1$ himself$^2$ off the ground, could he?
--
$^1$In a ...
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1answer
394 views
Walter Lewin Lecture 16 - Ball bouncing on wall?
I never did Physics in university and I consider that a mistake so I am correcting that now by teaching myself. To that extent I have been watching the MIT lecture videos by Walter Lewin and I am ...
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2answers
128 views
“Dark” quantities
I don't know much about the so-called dark matter, apart from what has been described in popular descriptions of the reasons for it being postulated.
My question is, is there dark momentum, dark ...
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1answer
70 views
Conservation of momentum in collision of two bodies
Suppose we have some ramp on wheels of mass $M$, standing on a
frictionless surface. A cart of mass $m$ moves with a certain velocity
$v$ towards the ramp. The cart moves up the ramp ...
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2answers
157 views
Firing machine question
Suppose we have a firing machine on a frictionless surface at point $x=0$. It fires a bullet of mass $m$ every $T$ seconds. Each bullet has the same constant velocity $v_0$. There's a body of mass ...
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3answers
174 views
Proof for $p=\gamma_Pmu$
As I'm reading about Relativistic Momentum, my book states the following:
$$p=m \frac{\Delta x}{\Delta t}=m\frac{\Delta x}{\sqrt{(1-u^2/c^2)}\Delta t}=\frac{mu}{\sqrt{1-u^2/c^2}}=\gamma_Pmu$$
...
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3answers
173 views
Simple elastic collision
If a particle with mass $m$ collides with a wall at right angles, and the collision is perfectly elastic. The particle hits the wall at $v\ ms^{-1}$. There is no friction or gravity.
So the particle ...
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2answers
102 views
A thought on definition of momentum
Well, this is a simple, basic and I think even silly doubt. The first time I saw the definition of momentum as $p = mv$ I started to think why this is a good definition. So I've read the beginning of ...
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202 views
Explanation for classic mechanics puzzle
I'm trying to figure out a nice way to describe to a kid the physics behind these experiments:
Assuming ideal conditions, we have a small boat with a sale, close to a lake's shore and a fan fixed on ...
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3answers
251 views
Train crash: are these situations alike?
I was just wondering... I believe that if a car travelling 50 miles per hour crashes into a wall, the result should be the same as crashing to another car also travelling 50 miles per hour (but in the ...
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2answers
3k views
Difference between momentum and kinetic energy
From a mathematical point of view it seems to be clear what's the difference between momentum and $mv$ and kinetic energy $\frac{1}{2} m v^2$. Now my problem is the following: Suppose you want to ...
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1answer
89 views
Hermitian Adjoint of differential operator
I came across this equation (identity) (Eq. 4 in this paper):
$\int(-i d\psi/dx)^*\psi dx = \int \psi^*(-i d\psi/dx) dx + id(\psi^*\psi)/dx\mid_{-\infty}^{+\infty}$
I have trouble proving it. I ...
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2answers
217 views
Small car colliding with large truck
A small car collides with a large truck. Why do both vehicles experience the same magnitude of force? Wouldn't the large vehicle experience less force than the small one?
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1answer
123 views
Total momentum of the Universe
What is the total momentum of the whole Universe in reference to the point in space where the Big Bang took place?
According to my reasoning (and a bit elementary knowledge) it should be exactly ...
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2answers
896 views
Do the physics in the FlyBoard video make sense?
If you haven't seen the video of the FlyBoard, please have a look: http://www.youtube.com/watch?v=Cd6C1vIyQ3w&feature=youtube_gdata_player
Yes, it's amazing, but do the physics make sense or is ...
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2answers
104 views
Does spacetime have momentum?
In what sense can it be said that spacetime possesses momentum? Can an experiment be envisaged to test this question?
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1answer
401 views
Elastic collision in two dimensions
Suppose a particle with mass $m_1$ and speed $v_{1i}$ undergoes an elastic collision with stationary particle of mass $m_2$. After the collision, particle of mass $m_1$ moves with speed $v_{1f}$ in a ...
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3answers
197 views
Should any theory of physics respect the principle of conservation of angular momentum or linear momentum?
Is it possible that a theory that can describe the universe at the planck scale can violate things that we now consider fundamental in nature?For example can it violate rotational and translational ...
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1answer
57 views
Quantum mechanical analogue of conjugate momentum
In classical mechanics, we define the concept of canonical momentum conjugate to a given generalised position coordinate. This quantity is the partial derivative of the Lagrangian of the system, with ...
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2answers
112 views
Movement of man and ladder and their center of mass
Suppose there is a massless frictionless pulley.
A rope over it carries a mass $M$ and on other side carries a ladder of mass $(M-m)$ and a man on that ladder, of mass $m$. Now the man starts ...
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1answer
116 views
Relativistic kinematics of particle decay
Suppose a particle decays to three other particles. The masses of all particles are assumed to be known and we work in the rest frame of the parent particle.
So there are 12 parameters for this ...
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1answer
119 views
Mass Shell in Light Cone Coordinates
I'm reading Zweibach's introduction to string theory, and don't understand one of his claims.
He defined the mass shell to be the set of points in momentum space s.t. $p^2+m^2 = 0$. Then the physical ...
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1answer
225 views
momentum conservation question involving a rocket and a spaceship [closed]
With the engines off a space ship is cruising at a velocity of 230m.s
It fires a rocket straight ahead at the enememy vessel. The mass of the rocket is 1300kg and the mas of the ship (not including ...
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1answer
717 views
Use the relative velocity formula to find v2f in terms of v1f?
Q:
A $0.150\text{ kg}$ glider is moving to the right ($+x$) on a frictionless, horizontal air track with a speed of $0.80\text{ m/s}$. It has an elastic collision with a $0.300\text{ kg}$ ...
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1answer
248 views
What is the linear momentum of an EM wave in a medium?
In free space, the linear momentum density of an EM wave is given by the Poynting vector $\vec S$ over the speed of light squared, $\vec g=\frac{\vec S}{c^2}$.
In a medium, $S$ is generally not ...
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1answer
139 views
General relativity and the conservation of momentum
I'm trying to understand the conservation of momentum in general relativity.
Due to the curvature of space-time by matters and energy, the path of a linear motion appears to be distorted.
Therefore ...
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0answers
135 views
Early stages of a computational model for object movement charting
We would like to build a computational model capable of accurately predicting the position of any object inside a chamber at any given time.
Inside the model we would have a number of smaller ...
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0answers
251 views
kinetic energy in collisions
We were hoping you could help us understand collision energy.
Vehicle A is driving West at 35mph and weighs 1437kg.
Vehicle B is driving North at 35 mph and weighs 1882kg.
Vehicle B crashes into the ...
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3answers
1k views
A spinning bullet
I know the rifling in a gun or rifle puts a spin on the bullet along the axis of trajectory. Now I don’t understand exactly what does it make the trajectory more stable and the travel grater?
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2answers
132 views
What does it mean if a body has kinetic energy?
What does it mean if a body has kinetic energy?
Does it mean that the momentum vectors of each particle of that body has the same direction?
What about angular momentum?
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2answers
104 views
Directionality of angular momentum
I was told that the sum of linear and angular momentum is conserved.
Given that angular momentum's direction as a vector is completely arbitrary (I believe there is no physical reason for choosing ...
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1answer
148 views
Rocket drive and conservation of momentum
I am currently reading through some lecture notes of Physics 1 and in a chapter about the dynamics of the mass point, there is an example covering the rocket drive.
Let $v$ be the velocity of the ...
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2answers
234 views
Connection between momentum and energy
What is the connection between momentum and energy?
Which of the answers is the correct?
A particle can have zero momentum but energy.
A particle can have zero energy but momentum.
...
