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
A jumper departs from an inclined plane with a velocity of 100km/h and no rotation. He wants to summersault while he is airborne within 2s.Based on the conservation of angular momentum, he will start tom rotate if his wheel's rotation is slowed down. His wheels are hollow...
Can momentum space also able to handle spin and polarizations?
I'm understanding it that in QM, you have position, momentum, spin, polarization as observables. Position and momentum can be equivalent via Fourier transform. So if you use momentum space instead of position, how do you handle...
HI
In a new report published the Thursday 26 October in the journal Science Advances, a team of physicists based in the UK, Germany, New Zealand and Canada describe how new research into "optical angular momentum" (OAM) could overcome current difficulties with using twisted light across open...
Homework Statement
Two beads with masses of M and m are threaded on a vertical loop with radius of R.
M is released without velocity from a height of 1.5R from the bottom of the loop.
The collision between the beads is completely elastic.
What is the smallest mass M that will make the second...
Homework Statement
Everything we know is in the picture.
There is no friction between the body and the wagon and between the wagon and the floor.
What will be the maximum height that the body will reach on the wagon? (Answer:0.008v02)
What will be the velocities of the body and the wagon once...
Homework Statement
Two balls with mass m and 4m collide at the location x=y=0 and stick. Their initial velocities just before the collision can be represented as v1=(i+j) v and v2=(j-i)v' respectively. Their final velocity vf makes an angle θ with the +x axis. Find v and v' in terms of vf and...
I read that kinetic energy may not be preserved, but momentum must always be preserved.
How can that be? If there's a loss in kinetic energy due to friction or heat, the velocities will be reduced thus momentum will be reduced?
I am working through Lessons in Particle Physics by Luis Anchordoqui and Francis Halzen; the link is https://arxiv.org/PS_cache/arxiv/pdf/0906/0906.1271v2.pdf. I am on page 11, equation 1.3.20. The authors have defined an operator ##L_{\mu\nu} = i( x_\mu \partial \nu - x_\nu \partial \mu)##...
Homework Statement
The dwarf planet Pluto orbits very ellipticaly... Pluto's nearest (perihelion) and farthest (apihelion) distances from the Sun are 30 AU and 50 AU, respectively. (One AU or Astronomical Unit=the mean distance from the center of the Earth to Astronomical Unit = the mean...
Homework Statement
A taxi car weighing 2000kg hits a stationary mini-van that has a mass of 2200kg. The taxi stops and the mini-van rolls and hits a stationary sports car with a mass of 1830kg. Their bumbers hit and they move together at 2.3m/s. What is the velocity of the taxi before the...
Homework Statement
Derive, using the canonical commutation relation of the position space representation of the fields φ(x) and π(y), the corresponding commutation relation in momentum space.Homework Equations
[φ(x), π(y)] = iδ3(x-y)
My Fourier transforms are defined by: $$ φ^*(\vec p)=\int...
Hi all, I have the following query:
I understand that the "make-up" of momentum probability density ##|\tilde{\Psi}|^2## has an effect on the motion of the spatial probability density ##|\Psi|^2##. For example, a Gaussian ##|\tilde{\Psi}|^2## centred far to the right will cause ##|\Psi|^2## to...
Homework Statement
We release a ball from a height h and it bounces for a time t. What is the value of k (the quotient of the ball's momentum before and after collision with the ground)?
Homework EquationsThe Attempt at a Solution
I'm kind of lost here. :/
[/B]
Homework Statement
A 10 g bullet traveling at 400 m/s strikes a 10 kg , 1.2-m-wide door at the edge opposite the hinge. The bullet embeds itself in the door, causing the door to swing open. What is the angular velocity of the door immediately after impact?
Homework Equations
p[/B]= mv
L = Iω...
Homework Statement
A comet orbits the sun. It's position in polar coordinates is given by, $$r(\phi)=\frac{1.8r_0}{1+0.8\cos{\phi}},$$ where ##r_0## is the position at closest approach. Its velocity at this point is given by ##v_0##. Use the concept of angular momentum to find the following...
Homework Statement
A cylindrical rocket of diameter 2R and mass M is coasting through empty space with speed v0 when it encounters an interstellar cloud. The number density of particles in the cloud is N particles/m^3. Each particle has mass m << M, and they are initially at rest.
Assume each...
One day Steve (68 kg) rolls into class on a skateboard. When he rolls in on the skateboard, he and the skateboard move at 2 m/s toward the windows in the room. Steve then jumps off the skateboard and he ends up moving at 1.0 m/s toward the windows of room. How fast and in what direction is the 1...
I read in several places that if, for example, a point particle exhibits uniform circular motion about the z-axis within an osculating plane not equal to the x,y plane, then the angular velocity still points along the z-axis, even though the angular momentum does not (it precesses about the...
Homework Statement
In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with a 0.40 kg puck B, which is initially at rest. Puck A moves at 4.2 m/s [W 30 N] . Find the final velocity of puck B.
Homework Equations
Conservation of momentum
Pythagorean theorum
The...
Homework Statement
[/B]
In an elastic head-on collision, a 0.60 kg cart moving at 5.0 m/s [W] collides with a 0.80 kg cart moving at 2.0 m/s [E]. The collision is cushioned by a spring (k=1200 N/m).
a) Find the velocity of each cart after the collision
b) Find the maximum compression of the...
Homework Statement
a)Two balls of equal masses undergo and elastic collision on a pool table. The final velocities of the two balls are v1=18m/s [S10W] and v2= 14m/s [S30E]. If the initial velocity of the first ball was w1=16m/s [S15E], what was the initial velocity of the second ball?
b)...
Homework Statement
Derive the relativistic Euler equation by contracting the conservation law $$\partial _\mu {T^{\mu \nu}} =0$$ with the projection tensor $${P^{\sigma}}_\nu = {\delta^{\sigma}}_\nu + U^{\sigma} U_{\nu}$$ for a perfect fluid.
Homework Equations
$$\partial _\mu {T^{\mu \nu}} =...
Homework Statement
Fast moving α particles of mass m make collisions in a cloud chamber with gas atoms of mass M and negligible initial velocity. After a collision, the velocities of the scattered α particles and the recoiling gas atoms are v and V respectively, the former being inclined at an...
Hello,
#1 As my teacher explained "T=F•r•sin<" all clear so far.
When i attempted to apply the formula it crossed my mind that the unit of T is (N•m), if so how do we solve for distence 0< r < 1.
#2 Another question if the unit is {(kg•m)/(s^2)}•m why did he represent moment with Newtons...
Homework Statement
A kid pushes a sled on ice that is smooth, level and essentially frictionless. The kid is 50kg, the sled is 10kg, he pushes the sled hard enough to give it a veloctity of 5m/s. How fast does he end up moving backwards on the ice when letting go of the sled?
Homework...
Hi all,
I recently learned the concept of Maxwell's speed distribution and became interested in how to use similar momentum distributions to study the probabilistic motion of a classical free particle. I have done some of my own reading on probabilities and distributions (no formal lessons yet)...
It's simple to everyone but me haha
1. Homework Statement
We toss an egg onto the floor, and it breaks. We toss an egg onto a pillow on the floor, and it does not break. The egg that does not break experiences a smaller:
A. Impulse
B. Change in momentum
C. Maximum ForceHomework Equations...
Homework Statement
Hello All,
I might be at best HS level physics understanding but I’m quick study and need guidance. I am in a debate with someone who thinks a body can be crushed to the point of dust. I’d like to know if a comparison can be made, basic ratio: Human crushed by a building at...
Homework Statement
Homework EquationsThe Attempt at a Solution ## \frac { - d \phi }{dt} = V ##
V denotes emf.
The current is in ## \hat \phi ## direction.
Magnetic force is along ## ~\hat s ## direction.
Where ## ~\hat s ## is the radially outward direction in cylindrical...
In the original EPR paper momentum was giving as an example of entanglement, but I don't see that discussed by any thread or papers for that matter, why is that. What is the technicalities of this entanglement for two electrons for example, is it also instantaneous and why is it not used to...
Homework Statement
Homework Equations
E = γmc2
p = γmv
K = E - mc2
E2 = c2p2 + m2c4
The Attempt at a Solution
I have completed most of this question, but I am struggling to get the required result to the final part of the question.[/B]
Hi all,
My question is in reference to the following paper: https://arxiv.org/pdf/1202.1783.pdf
In equation 3.8, the author computes an order-of-magnitude approximation of probability of measuring negative momentum from the following wavefunction:
$$
\Psi_k =\sum_{k=1,2}...
Homework Statement
A particle in one dimension is in the ground state of the potential well given by V(x)= 0 for |x|<L/2 and infinite otherwise. Let P+ be the probability that the particle is found to move along the positive x direction and p be the magnitude of the momentum for that state of...
Homework Statement
A hockey player hits a slap shot, exerting a constant force on a 3.06 kg puck for 0.06 seconds. What is the change in momentum of the puck?
Homework Equations
Impulse = Mass x (Change in velocity) = Force x time
(I think that’s all needed? Most likely missing one.)
The...
I have a question about momentum vs kinetic energy.
For example, a block C with velocity Vc and mass=2m hit a block B with mass=m at stand still on a LEVELED frictionless track( no change of potential energy). The two block stick together and move at velocity Vcb. Find the relation of Vc vs...
Homework Statement
Two blocks with masses 1 kg and 4 kg respectively are moving on a horizontal frictionless surface. The 1 kg block has a velocity of 12 m/s and the 4kg block is ahead of it, moving at 4 m/s. The 4 kg block has a massless spring attached to the end facing the 1 kg block. The...
Homework Statement
this has been bugging me for a while now the angular momentum about any point p is given as
##
\vec {L_p} = \vec {R_{cm,p}} \times \vec {P_{cm}} + L_{cm}\\
##
now if the body precessing around z axis and spinning about its own axis then angular velocity of body in lab...
1.
Two particles P and Q are moving in opposite directions along the same horizontal straight ine. Particle P is moving due east and particle Q is moving due west. Particle P has mass 3m and particle Q has mass 2m. The particles collide directly. Immediately before the collision, the speed of P...
Homework Statement
A system has total angular momentum L about an axis O. Show that the system's angular momentum about a parallel axis O' is given by L'=L-h×p, where p is the system's linear momentum and h is a vector from O to O'.
Homework Equations
L=r×p or considering a mass element...
Homework Statement
Hello,
Here is a multiple choice question I would like to be clarified.
Suppose that the angular momentum of a system can take the values 0, 1, 2. One carries out a measurement of ##J_z##,the state of the system will:
##a##-Be perfectly known if the result is 0
##b##-Be...
Homework Statement
A uniform thin rod of Length L and mass M can freely rotate about a point 0 and is at rest in at the vertical. A ball of mass m on a light string of length R, which is also attached about the pivot is deflected by a small angle from the vertical and let go of.
If the...
Hello,
Suppose that the angular momentum of a system can take the values 0, 1, 2. One carries out a measurement of ##J_z## on this system.
What can be said about the state of the system after the measurement? To what extent can it be perfectly certain if ##J_y## and ##J_x## do not commutate...
Hi all,
I understand the mathematics behind special relativity pretty well, but I only have a bare conceptual understanding of general relativity. My understanding is that energy, momentum and stress (as described in the energy-stress tensor) are what contribute to space-time curvature and...
Hi everyone, hopefully someone will be able to point me in the right direction with this problem, I get as far as combining the two equations together and no matter how I rearrange them they don't seem to cancel nicely and leave me with an awful quadratic, I can find vx, but the question...
Homework Statement
A car of mass 1500 kg is at rest on a platform of mass 3000 kg, which is also at rest. The platform has frictionless wheels attached to its bottom. The whole system is initially at rest. The car starts to move forward at a speed of 5.0 m/s with respect to the ground...
Can a reasonable observable operator be defined which measures a two-component observable, first component for the approximate coordinate and the second for the approximate momentum (so that the precision of each measurement do not contradict Heisenberg inequality)?
I am actually thinking of...
Water is flowing inside a garden hose. The hose is bent at some point, i.e., it has the shape of L. What is the direction of the force applied by the water on the hose around the bend? (Let's say that one of the arms of the L goes along +x direction and the other arm goes along the +y direction...
One of the reasons I've been so stumped about learning about angular momentum in QM, is that in my classical physics class we only applied it to circular motions. Hence, while I am aware that angular momentum is connected to spherical harmonics, the orbital shapes (besides s) isn't really...
Hi,
good afternoon
the problem is this: This device was assembled with the purpose of calculating the torque of a small motor. It measures the force F through a charge cell. The calculations performed for the moment were made using the data provided by the load cell and distance "d". However...