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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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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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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2answers
372 views

Translation Invariance without Momentum Conservation?

Instead of the actual gravitational force, in which the two masses enter symmetrically, consider something like $$\vec F_{ab} = G\frac{m_a m_b^2}{|\vec r_a - \vec r_b|^2}\hat r_{ab}$$ where $\vec ...
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1answer
378 views

What is the result of a classical collision between THREE point particles at the same precise instant?

Classical Mechanics is said to be deterministic, a statement that nearly always is followed by that quote from Laplace, something like If at one time, one knew the positions and velocities of all ...
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3answers
701 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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3answers
1k views

Can conservation of momentum related to Newton's first law?

I know this is a scrap of thought, but the first law states that (from Wikipedia): If an object experiences no net force, then its velocity is constant Is it describing the conservation of ...
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2answers
179 views

Is air drag equation in term of momentum still valid?

This is the known equation of air drag: $$m{\bf a}=mg-\mathcal D=mg-b{\bf v}.$$ Considering this, is air drag equation in term of momentum still valid? $$m{\bf v}=mv_g-b{\bf r}.$$
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591 views

Classical mechanics and the speed of a train-mosquito collision, when perfectly rigid bodies

This is all under the assumption that they are perfectly rigid bodies: A train is moving at 300m/s. A mosquito is moving directly towards it, head-on, at 4m/s. When the mosquito and the train ...
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1answer
991 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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0answers
77 views

about wavefunction and vector entries

I am beginer of physics and I am studying some very fundamental idea of quantum mechanics by myself. In the introducing book I am reading, there is an example to show a particle diffraced by a slit or ...
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3answers
291 views

Displacement with zero velocity

I know that we can rotate a deformable object using internal forces only in space. Thus we can cause an angular displacement without the use of any external forces. The following youtube video shows ...
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1answer
157 views

4-momentum and an $y$ component of momentum

I have 2 coordinate systems which move along $x,x'$ axis. I have derived a Lorentz transformation for an $x$ component of momentum, which is one part of an 4-momentum vector $p_\mu$. This is my ...
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2answers
461 views

Why is the “canonical momentum” for the Dirac equation not defined in terms of the “gauge covariant derivative”?

The canonical momentum is always used to add an EM field to the Schrödinger/Pauli/Dirac equations. Why does one not use the gauge covariant derivative? As far as I can see, the difference is a factor ...
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2answers
172 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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4answers
811 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
154 views

Spring coupled platforms & conservation of momentum - can it be solved with freshman physics?

This question came up as an exercise in a first year undergraduate course I was a TA for. It turned out to be a lot more difficult (impossible?) than anticipated... Two platforms of mass $M_1$ and ...
8
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3answers
781 views

Intuitively Understanding Work and Energy

It is easy to understand the concepts of momentum and impulse. The formula $mv$ is simple, and easy to reason about. It has an obvious symmetry to it. The same cannot be said for kinetic energy, ...
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3answers
510 views

Does the canonical commutation relation fix the form of the momentum operator?

For one dimensional quantum mechanics $$[\hat{x},\hat{p}]=i\hbar $$ Does this fix univocally the form of the $\hat{p}$ operator? My bet is no because $\hat{p}$ actually depends if we are on ...
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1answer
2k 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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1answer
146 views

Integration of constant: $\int dp = \Delta p$ in impulse formula

In University Physics, it has something like: $$\int \sum F dt = \int \frac{dp}{dt} dt = \int dp = \underbrace{p_2 - p_1}_{\Delta p?}$$ But I thought $\int dp = p$? Though my maths is really rusty ...
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0answers
38 views

Elastic Collision Between Two Objects [duplicate]

Possible Duplicate: Elastic Collision And Momentum I've already asked this question, Elastic Collision And Momentum, but I didn't find the answer particularly helpful--sorry, I don't mean ...
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1answer
779 views

Elastic Collision And Momentum

The question I am working on is, "Two blocks are free to slide along the friction-less wooden track shown below. The block of mass $m_1 = 4.98~kg$ is released from the position shown, at height $h = ...
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1answer
199 views

Analysis of the impulse of 2 colliding carts under the effect of magnetic repulsion

Hi there! I have a question about an experiment that was conducted. It is related to momentum. 2 carts were put on a track on opposite sides. They were then propelled towards one another at ...
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2answers
872 views

Photon energy - momentum in matter

$E = h\nu$ and $P = h\nu/c$ in vacuum. If a photon enters water, it's frequency $\nu$ doesn't change. What are its energy and momentum : $h\nu$ ? and $h\nu/c$ ? Since part of it's energy and momentum ...
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1answer
81 views

Physics Impulse

This is the problem I am dealing with: "One of the functions of an automotive air bag is that it lengthens the collision time. Without an air bag, suppose the 100Ns impulse of a collision is taken up ...
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1answer
245 views

Momentum And A Car Collision

I am studying an example problem, concerning the very topic mentioned in the title. In this example problem, a car has a head-on collision with the wall; the initial and final velocity are known, as ...
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1answer
101 views

A Decrease In Momentum?

The specifics of a question I am working on are, "After a 0.280-kg rubber ball is dropped from a height of 1.80 m, it bounces off a concrete floor and rebounds to a height of 1.45 m." Why doesn't the ...
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1answer
524 views

Momentum And Energy Problem

The information to the question is, "A $59.0~kg$ boy and his $38.0~kg$ sister, both wearing roller blades, face each other at rest. The girl pushes the boy hard, sending him backward with a velocity ...
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1answer
945 views

Relative Velocity and Momentum

The question is, "A $45.5~kg$ girl is standing on a $140~kg$ plank. Both originally at rest on a frozen lake that constitutes a friction-less, flat surface. The girl begins to walk along the plank at ...
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1answer
721 views

What is the linear momentum of an inelastic and elastic collision?

The arrows in the figure represent the linear momentum of two balls before they collide. If the collision is perfectly inelastic, find the linear momentum after the collision. If the collision is ...
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4answers
2k views

Relativistic momentum

I have been trying to derive why relativistic momentum is defined as $p=\gamma mv$. I set up a collision between 2 same balls ($m_1 = m_2 = m$). Before the collision these two balls travel one ...
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1answer
213 views

Conservation of momentum with MOND

Assuming as true the phenomenological MOND law for low accelerations ($< 10^{-10} m s^{-2} = a_0$), and considering a small mass $m$ attached to a larger mass $M$ by a faint spring (let's think of ...
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125 views

Non-relativistic Kepler orbits

Consider the Newtonian gravitational potential at a distance of Sun: $$\varphi \left ( r \right )~=~-\frac{GM}{r}.$$ I write the classical Lagrangian in spherical coordinates for a planet with mass ...
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1answer
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Violation of Newton's 3rd law and momentum conservation

Why and when does newtons 3rd law violate in relativistic mechanics? Check this link http://www.animations.physics.unsw.edu.au/jw/Newton.htm.
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2answers
258 views

Conservation of Linear Momentum with respect to a given direction

Is linear momentum conserved in any direction? More specifically, if you project all momentum vectors in a system onto another vector, will momentum be conserved? I know that momentum is conserved ...
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2answers
2k views

Inelastic collision and conservation of linear and angular momentum

Is it possible for two spheres (a & b) to have an inelastic collision with BOTH the total linear and angular momentum preserved? I'm doing some physics simulation of some spheres attracting each ...
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4answers
764 views

Find total energy and momentum of an moving electron in a rest frame

I have an electron moving with speed $u'$ in a frame $S'$ moving with speed $v'$ relative to a rest frame $S$. How do I find the total energy and momentum of the electron in the rest frame $S$? I ...
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3answers
882 views

Same momentum, different mass

The question is: if A bowling ball and ping pong ball are moving at same momentum and you exert same force to stop each one which will take a longer time? or some? which will have a longer ...
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1answer
472 views

Intuition of Impulse Formula $J = \sum F \Delta t$

I understand that $$\begin{align} J = \sum F \Delta t &= \Delta p \\ \sum F &= \frac{\Delta p}{\Delta t} \\ &= \frac{mv_2 - mv_1}{\Delta t} \\ &= m \cdot \frac{\Delta v}{\Delta t} \\ ...
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1answer
272 views

Controlling the outcome of a quantum measurement through translational entanglement

According to the paper: A. S. Parkins and H. J. Kimble, Phys. Rev. A 61, 52104 (2000). http://pra.aps.org/abstract/PRA/v61/i5/e052104 You can entangle position and momenta of two atoms by using ...
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4answers
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Intuitive explanation of why momentum is the Fourier transform variable of position?

Does anyone have a (semi-)intuitive explanation of why momentum is the Fourier transform variable of position? (By semi-intuitive I mean, I already have intuition on Fourier transform between ...
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2answers
533 views

Center of mass of a car

This might be little of the track but my question is more on possibility of application of principle of center of mass. The probability of a vehicle overturning depends more on the level of center of ...
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1answer
464 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 ...
3
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3answers
1k views

Newton's 3rd Law: How can I break things?

If I punch a wooden board hard enough and it breaks in two, has the board still exerted a force of equal magnitude on my fist? When the board breaks in two due to my force, the halves have a ...
0
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1answer
161 views

Would synchronized dancing be a good way to describe entangled atoms to a laymen?

I was talking my professor about entanglement swapping between light and matter and it is briefly described here: You start out with a crystal capable of doing parametric down conversion of incoming ...
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3answers
511 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
277 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
2k 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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3answers
454 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
821 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 ...