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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Why does rubber ball bounce back while iron ball doesn't?

Suppose there are two balls, one of rubber and the other metallic. There are of the same mass and are thrown on a wall with the same velocity. Why does a rubber ball bounce back while a metallic ball ...
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Why is there no relation between kinetic energy and momentum in collision of two bodies? [duplicate]

The statement that baffles me: During most of the collisions, part of the kinetic energy evolve as heat, nevertheless momentum is still conserved. Ok, the statement may be true. But what ...
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1answer
54 views

Swinging onto a Hill

I was just watching the movie "Frozen" (not the Disney one), and they were trapped in a ski lift 50 feet off the ground. They had to jump. My question is, when they jump, should they swing on the ...
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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 ...
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What is a rocket engine thrusting against in space?

I know Newton's third law of motion might be the answer for this but still I am wondering how the rockets could thrust in the empty space and move in the opposite direction. I guess an astronaut ...
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Does leaning (banking) help cause turning on a bicycle?

I think it's clear enough that if you turn your bicycle's steering wheel left, while moving, and you don't lean left, the bike will fall over (to the right) as you turn. I figure this is because the ...
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4answers
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Can momentum be conserved in a perfectly elastic collision?

I am taking for granted that when we say that something is conserved it is understood 'in its full integrity'. Energy is represented by a scalar J, and is conserved in elastic collision. momentum ...
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2answers
92 views

How to show that $\partial S/\partial q=p$ without variation of $S$?

I'm trying to get some understanding in treating action $S$ as a function of coordinates. Landau and Lifshitz consider $\delta S$, getting $\delta S=p\delta q$, thus concluding that $$\frac{\partial ...
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1answer
318 views

Difference in “momentum” names in Lagrangian mechanics

In the context of Lagrangian formulation of classical mechanics, the following names keep occurring in most textbooks, which confuse me a lot, are they different in any way? Momentum Generalized ...
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330 views

A question regarding 3 bodies connected as a system

Let us consider three bodies of equal mass connected to each other with 2 ideal strings of length l. The three bodies are placed in a straight line In this arrangement there is 1 body connected to 2 ...
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1answer
107 views

A question regarding collisions

Let us consider a system of 2 identical spherical bodies connected by a massless string that is taut. If one body is placed at the origin then the other is placed at some coordinate $(x,y)$. The ...
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Interpreting some domain issues of (potential) momentum operators

In the context of mathematical quantum mechanics, a well known no-go theorem known as Hellinger-Töplitz tells us that an unbounded, symmetric operator cannot be defined everywhere on the Hilbert space ...
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Center-of-mass frame for massless particles

Given a scattering event where a photon and electron go in and a photon and electron come out, what is the center of mass frame? I'd say, since the photon has no mass, it's the rest frame of the ...
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6answers
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What is the relationship between force and momentum in collisions?

I know that $ \Sigma F = \Delta mv/\Delta t$. But if we had a marble that moves in a straight line at a constant velocity and colloids with another marble. Because of the law of conservation of ...
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2answers
184 views

Add weight in front or behind the moving wheel?

Consider a wheel with bearing and axle bar rolling on level ground. If I want to help the wheel continue moving longer(or faster speed), should I add weight by moving the rider body in front or behind ...
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1answer
355 views

In QED, why is the $e^- + e^+\leftrightarrow\gamma$ process forbidden on-shell?

QED has a vertex that couples a single photon to two fermions. This vertex describes the annihilation of an electron-positron pair into a photon. Why is this process forbidden for all three particles ...
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336 views

Relation between the conservation of Energy and the conservation of Momentum?

I just learn about the momentum and it conservative attribute in a closed and isolate system and there is something I don't understand when I relate it to the conservation of the energy Considering ...
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Conservation of Mathematical Constraints when deriving Energy and Momentum from $F=ma$

Background: Starting from $F = ma$, integrating with respect to time, and using basic calc, one can derive $\int Fdt = m (v_f - v_i)$ Starting from $F = ma$, integrating with respect to distance, ...
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0answers
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Momentum operator in Dirac formalism

Could you derive the momentum operator as follows: Since $\mathcal{T}(\Delta x)=\exp(-ip_{x} \Delta x/ \hslash)$, if we set $\Delta x=x-0$ then it follows that $\left \langle x\right | \mathcal{T^{\...
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2answers
261 views

Effect of movements of astronauts on International Space Station

I know that astronauts move in and around in ISS. When they move they also touch the modules of ISS and sometimes they apply force on the module to move. When this happens, as far as I know it affects ...
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1answer
206 views

Where does the partial derivative come from in Sakurai's derivation of the momentum operator?

How is the momentum operator derived in Dirac formalism? I am reading Quantum Mechanics by Sakurai and he gives the following derivation. But I don't understand how he goes from the third equation to ...
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1answer
4k views

How do I show the fractional change in Kinetic Energy in a completely inelastic collision?

Given the formula $$\frac{{\Delta}(KE)}{KE_i}=\frac{(KE_f-KE_i)}{KE_i}=\frac{-M}{(m+M)}$$ Now I know these that the conservation of momentum is always applicable. Also I understand that $$KE=\frac{...
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Special Relativity: Finding the Euler Lagrange of a massive particle

Knowing that $$\tag{1} L= -mc\sqrt{-\eta_{ab}\frac{d\xi^a}{d\lambda}\frac{d\xi^b}{d\lambda}}$$ we get $$\tag{2} p_a=\frac{\partial L}{\partial(d\xi^a/d\lambda)} = m\eta_{ab}u^b.$$ How come? If I ...
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2answers
627 views

Question relating to energy transfer in between two particles

How would I go about calculating the maximum kinetic energy transferred from one particle when it forms an elastic collision with another particle. For example, if I had two billiards one with mass m ...
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1answer
543 views

Impact force in a fall

I'm a climber and I constructed myself an anchor that I fixed to a rock wall. To test it, I hooked to it a 12mm in section steel cable with a length of 2,8m and a concrete block of 30kg to the other ...
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Four-momentum, four-velocity, energy

If given the four-momentum of any particle monitored by an observer as: p = $p^\hat{α}e_\hat{α}$ using unit vectors in observer’s reference frame and u = $e_\hat{0}$ then I get I'm just ...
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The elusive difference between impulse and momentum

1) In classical mechanics, impulse is the product of a force, F, and the time, t, for which it acts. The impulse of a force acting for a given time interval is equal to the change in linear ...
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1answer
476 views

Question on the negativity of the coefficient of restitution

I was trying to solve a Mechanics question on Momentum. Here is the question : Two small smooth spheres A and B have equal radii and have masses m and km respectively. They are moving in a ...
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0answers
121 views

Momentum of capacitor in a uniform magnetic field

We are observing ideal, charged, parallel plate capacitor placed in uniform magnetic field parallel to plates. Whole system is at rest and isolated (we have forces that hold plates separated, but net ...
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3answers
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When is momentum not conserved?

What are some common examples where momentum is not conserved? This question arose in my mind when I read that a ball dropped from a height penetrates into a bed of sand and that momentum is ...
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Punching - Force or Momentum?

If I want to punch a person inflicting maximum damage, what do I need to care about? My force of punching, i.e, do I need more acceleration? Or do I need momentum, i.e my velocity for punching?
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Can conservation of momentum and conservation of energy explain every possible event in the Universe?

I heard my friend, a researcher, say that we can, in theory, explain every event happening in the universe using the Conservation of momentum and energy. He added that we may not be able to do that "...
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Momentum of electron problem [duplicate]

Recently, my friend bemused me with a question related to the momentum of an electron. The confusing logic is stated below: Since an electron is a particle and according to classical physics, we know ...
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2answers
143 views

Recommendation on ADM mass and Bondi mass

I want to learn some advanced topics in GR, such as ADM 4-momentum and Bondi 4-momentum. However nearly no textbooks on GR contain this area, such as Wald, MTW, Hawking, Carroll and Zee's. Can anyone ...
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1answer
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Directional derivatives in the multivariable Taylor expansion of the translation operator

Let $T_\epsilon=e^{i \mathbf{\epsilon} P/ \hbar}$ an operator. Show that $T_\epsilon\Psi(\mathbf r)=\Psi(\mathbf r + \mathbf \epsilon)$. Where $P=-i\hbar \nabla$. Here's what I've gotten: $$\begin{...
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1answer
126 views

Why do safety helmets have a softer inner layer nearer the head?

I know that when an object collides onto the helmet, it causes an inelastic collision so that energy is absorbed by the structure of the helmet, so what exactly does the softer inner layer do? Does it ...
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1answer
187 views

How similar is comparison between the principle behind Newton's Cradle versus AC Current moving down a transmission line?

Anyone who has taken high school physics has seen the following assembly. You drop one ball from the left hand side and the ball from the farthest right hand side gets knocked away. This is to ...
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2answers
143 views

Is the energy of momentum stored physically? [closed]

While an object is moving, relativity will say it weighs more, especially so as it approaches light speed. The increase in energy is then easily sensed as an increase in mass (Almost as a rock in ...
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2answers
250 views

Momentum vector transformation

I am confused about the way momentum vector transforms in the following case: $$q_k \to q_k'= q_k + \epsilon f_k(q)$$ The Jacobian is thus $\Lambda_{ij} = \frac{\partial q'_i}{\partial q_j} \approx \...
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1answer
190 views

Motivating the ansatz for the infinitesimal translation operator

I'm reading Sakurai's Modern QM right now and in the first chapter he states a number of conditions required for a translation operator: unitarity, $$T(\mathrm{d}\mathbf{x})T(\mathrm{d}\mathbf{x^\...
2
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2answers
866 views

Will I be able to push a small object in front of me in the outer space?

Imagine I am standing on Earth, and pushing a tennis ball away from me. The ball moves. If it is very heavy, I will move back instead of the ball. Now consider the same scenario in outer space, where ...
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3answers
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Different results to a basic question ( Newton's law and perservation of momentum)

Trolley with mass of $m_0=1 \ kg$ is moving without friction on the railway track. It is raining so there is a constant mass flow of water $\Phi_m=0.1\ kg/s$. Constant force $F=0.1 \ N$ is ...
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1answer
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What formula connects the moment of inertia and angular velocity? [duplicate]

I need to determine angular velocity of a disc when a man with given mass and speed whacks on the edge of it. I calculated the total moment of inertia of disc and body, how do I calculate the ...
5
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3answers
2k 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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4answers
485 views

Since everything with mass exerts a gravity force on everything else, why do objects float in outer space?

For example, if you were to go out into deep space, and just slow down and stop your rocket. Everything inside the rocket that's not strapped in, starts floating. Why is that if every object has mass ...
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2answers
219 views

What moves an object? Momentum or Kinetic Energy? [duplicate]

What exactly makes an object move? Momentum is $\vec p= mv$ where $m$ is mass of an object and $v$ is the velocity of an object, and as a result of this when I fire a bullet the bullet may travel much ...
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0answers
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The relationship between angular and linear momentum

Why is orbital angular momentum not 0 when spin and linear momentum are not collinear? Why can it be 0 when spin and linear momentum are parallel? Like in the example of a scalar field at rest ...
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2answers
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Does a reflection still transfer momentum to an mirror?

I have been recently wondering, if I take a powerful enough energy source (photon) and I have an perfect mirror exactly in front of it and assume an "emitter" shot the light towards the mirror. As ...
3
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1answer
422 views

Conservation of linear momentum, when is it conserved?

Will Linear momentum be conserved in a non-inertial frame of reference? In other words what is the fundamental condition for linear momentum to be conserved? Also which is more fundamental- Newton's ...
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Is the canonical momentum conserved when a particle moves in magnetic field?

Here is a question about the canonical momentum that I had asked some days ago, but I still have one point that I am not understand. Considering a particle moves in a magnetic field with charge $q$ ...