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 single electron atom has the outer electron in a 4f1 excited state. Write down the orbital and spin angular momentum quantum numbers and the associated magnetic quantum numbers for this state.
Homework Equations
I don't think there is any relevant equations. I think it...
Homework Statement
I have an issue with understanding the idea of generalised momentum for the Lagrangian.
For a central force problem, the Lagrangian is given by,
$$L = \frac{1}{2}m(\dot{r} ^2 + p^2 \dot{\phi ^2}) - U(r)$$
with ##r## being radial distance.
The angular momentum is then...
I am trying to create a momentum trap to calculate the velocity of a projectile when it hits the trap. It essentially consists of a plate if known mass at the bottom of a pendulum of known radius. When the projectile hits the plate, the degrees that the pendulum rotates are recorded. I believe...
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I am trying to design and perform a physics lab. It needs to show the relationship between torque and angular momentum. I have gotten as far designing a 4" PVC coupling and have it on a ramp. I am not sure where to go from here.
Homework Statement
A school playground has a carousel, which is simply a circular platform that can rotate around its center axis with negligible friction. This carousel has radius r=1.6 m and rotational inertia I= 177m^2kg. Suppose you are standing beside the carousel which is already spinning...
Homework Statement
A hydrogen atom is in the 7f state.
What is the magnitude of its orbital angular momentum?
Homework Equations
L=sqrt(L(L+1)hbar
The Attempt at a Solution
L= Sqrt(3(3+1)Hbar)
1.41hbar (we want J*S)
1.41*1.054*10^-34
1.47*10^-34J*S
Given a wave function $$\Psi(r,\theta,\phi)=f(r)\sin^2(\theta)(2\cos^2(\phi)-1-2i*\sin(\phi)\cos(\phi))$$ we are trying to find what a measurement of angular momentum of a particle in such wave function would yield.
Attempts were made using the integral formula for the Expectation Value over a...
Homework Statement
Lee is riding on her 6 kg skateboard with a constant speed of 2 m/s. She jumps off of her skateboard and continues forward with a velocity of 4 m/s relative to the ground. This causes the skateboard to go flying forward with a speed of 18.5 m/s relative to the ground. What is...
Homework Statement
I need to find the intial velocity of a ball, given the angle the pendulum bob swings through.
I need to derive this equation.
[/B]
V0=4.43mtotalL1/2{1-cosΔθ}1/2/mball
Homework EquationsThe Attempt at a Solution
I have barely any attempts since I can't even think where to...
Homework Statement
Why is the magnitude of Angular Momentum for an elliptical orbit as such?
$$l = mr^2\dot{\phi}$$
where ##\dot{\phi}## represents angular momentum.
I have always assumed that angular momentum was $$l = r \times P = mr \times V = mrVsin(\theta) = mr^2\dot{\phi} sin(\theta)$$...
Homework Statement
You decide to design a bicycle that will have only 3/4 of the angular momentum of the original wheel when both wheels are traveling along a road at the same velocity. The original wheel had a diameter of d1=37cm and rotational inertia of I1=0.32 m2kg. If your new wheel has a...
1. The problem statement
Consider a particle of mass m under the action of the one-dimensional harmonic oscillator potential. The Hamiltonian is given by
H = \frac{p^2}{2m} + \frac{m \omega ^2 x^2}{2}
Knowing that the ground state of the particle at a certain instant is described by the wave...
https://drive.google.com/file/d/1Z-avhDqYbxDtMzk6Rv_NES7rIvDmzMPz/view?usp=drivesdk 2.conservation of angular momentum
3.for the above question I tried applying conservation of angular momentum about the point of contact where the cyclinders touch each other but my answer does not match with...
Homework Statement
Derive the differential momentum equation: dp=-\rho udu.
Homework Equations
\oint_{ CS}^{ } \rho \vec{U}(\vec{U}\cdot \vec{n})dA=-\oint_{ CS}^{ } p\vec{n}dA for steady state flow...
The Attempt at a Solution
I tried to solve it like in the attached picture, but can someone...
A person standing on a stationary friction-less turntable spins a bicycle wheel with the rotation axis of the wheel in the horizontal direction, thus the initial angular momentum is in the horizontal direction (x - axis), say to the right. Now suddenly the person turns the axis of rotation of...
Homework Statement
In my reference frame, I see two carts collide. Both cart A and Cart B have a mass of 2 kg. Cart A has initial velocity v= 3 m/s i-hat + 2 m/s j-hat, cart B has initial velocity v= 3 m/s I-hat + 4 m/s j-hat. 12 J are released in the collision.
In previous parts of this...
Homework Statement
A uniform thin rod of length ##2l## and mass ##m## lies on a horizontal table. A horizontal impulse ##J## is given to the rod at one end. There is no friction. The total kinetic energy of the rod after impulse will be ?
Homework Equations
##Jl=I\omega##
##J=mv_{cm}##...
I understand for linear momentum the measure of the dificulty to take a body to the rest. But when I do the next exercises, I find that it requires less force for one body compared to the other with same linear momentum.
Can someone explain me what to understand in an intuitive way what to...
Homework Statement
According to the Big Bang model of cosmology, the universe has been expanding since some initial time (call it t = 0) when the temperature was infinite. At early times, the temperature T scales as t^1/2 . The current temperature is about 3K. Consider the part of space which...
Homework Statement
Three small, identical 0.70-kg pucks are attached to identical 0.50-m strings, tied together at a common center as shown in (Figure 1) . Pucks are whirled in circular motion at angular speed 3.0 s-1
What is the magnitude of the angular momentum of the system about the...
Hi,
Apologies if this questions is really easy but it is something quite subtle which is annoying me. In my book of quantum physics it gives a wave function of definite momentum:
ψ = Aeipx/ħ
It goes on to say that since there is a momentum 'p' in the exponential then the momentum is known...
Homework Statement
In the figure, a 0.400 kg ball is shot directly upward at initial speed 58.3 m/s. What is its angular momentum about P, 1.42 m horizontally from the launch point, when the ball is (a) at maximum height and (b) halfway back to the ground? What is the torque on the ball about P...
Homework Statement
A disk with a rotational inertia of 8.38 kg·m2 rotates like a merry-go-round while undergoing a torque given by τ = (5.03 + 1.01t) N · m. At time t = 1.00 s, its angular momentum is 6.57 kg·m2/s. What is its angular momentum at t = 3.00 s?
Homework Equations
dL/dt= T...
Hello guys.
So this is less about about the physics problem and more about the concepts behind it. I don't need help with any solution but I am framing my questions around the example given.
So there are two steel balls with equal mass that are hanging from a point by a string. Both strings are...
It explains very well many aspects of the Universe.
Why should there be any angular momentum though?
The idea that the Universe is itself intrisically rotating doesn't make sense.
Good evening,
Does anybody know how to get the units of momentum flux?
Momentum = kg m s−1
Flux = m−2 s−1
Somehow, I should end up with kg m-1 s-1
(kg m s−1) m−2 s−1 = kg m−1 s−1
However I end up with kg m-2 s-2
Is there anybody that knows what I'm doing wrong? :)
Homework Statement
A rocket, weighing 43,600N, has an engine that provides an upward force of 120,000N. It reaches a maximum speed of 860 m/s. For how much time must the engine burn during launch in order to reach this speed?
Homework Equations
p=m*Δv
i=F*t
The Attempt at a Solution
I started...
Homework Statement
Three freight cars of equal mass are coupled together. The freight cars are traveling at 6.7m/s down a straight track when they collide with two more stationary identical cars. If all five cars are coupled together after the collision, then what is their speed if they are on...
I need help with an equation for the angle of the legs of a swing. I am building a swing. It is only 4 feet high, it is an indoor apartment swing for my son. I would like to know what the minimum legs angle would need be to support swinging 25 pounds in a 180 (probably less) arch. And if I...
Homework Statement
What is the Average Force between m1 and m2. Show all work.
Note that the masses are both at rest, and begin to push off of each other in opposite directions.
Their velocity is measured when they reach 20cms distance. (I calculated the velocity when they reached this point...
Hi there, I am doing a physics assignment. I had to use a program called tracker to simulate the movement of a puck.
So I just need some help to see if anyone can figure out what I've done wrong as something isn't making much sense. Let's jump right into it.
When the puck moves down and hits...
Why the tangential velocity of a particle increase if there are no external torque acting on it and its angular momentum is conserved?
I know that L = I.ω (angular momentum equals moment of inertia times angular velocity)
and v = ω.r (tangential velocity equals angular velocity times the...
Dear Members,
I was going through some video lecture (Quantum Mechanics) when I encountered a definition of momentum as shown in the attached picture.
I do not understand how iota and ħ is ignored ? There are some negligible terms after plus sign. What are those ? In short how they have...
Homework Statement
A two-stage rocket is traveling at 4500 m/s before the stages separate. The 3000-kg first stage is pushed away from the second stage with an explosive charge, after which the first stage continues to travel in the same direction at a speed of 3000 m/s . How fast is the...
Homework Statement
[/B]
A rocket that starts at rest with mass M ejects exhaust at a given speed u. What is the mass of the rocket (including unused fuel) when its momentum is maximum? What is the mass when its energy is maximum?
Homework Equations
[/B]
p = mv
The Attempt at a Solution...
- This is the situation provided where it has to be demonstrated that linear momentum is not conserved or unrealistic. My assumptions are: there's no friction due to how Godzilla is moving, the sand is acting as a lubricant. Velocity is constant. This is an elastic collision. I also guess that...
Homework Statement
A satellite is in a circular orbit passing over the North and South geographical poles as it orbits the Earth. It has a mass of 2200kg and its orbit height is 870km above the Earth's surface. What is the change in momentum of the satellite from when it passes over the...
Homework Statement
There are two objects m and 2m and Force F is applied on both objects. They move a certain distance X. Which one have greater momentum and find out 2m has √2 times more momentum than m.
Homework Equations
momentum P=mv
The Attempt at a Solution
2m has greater momentum...
Homework Statement
We did a lab where we had one cart with an unknown mass stationary on a friction-less surface. Another cart with a mass of 378.9g, was pushed down the track (which moves at a constant speed due to the friction-free surface) and collides with the second cart - so it is a hit...
Given that position and momentum are Fourier conjugates, what is the derivation for the equation ##\hbar \vec{k} = m \vec{v}##, where momentum-space momentum is defined as ##\hbar \vec{k}## and position-space momentum is defined as ##m \vec{v}##?
γ+2D ----> 1H + 1n
In this photonuclear reaction, is it possible to write the momentum balance equation as it follows,
MHvH = Mnvn
It somehow seems to wrong to me, since the incoming photon has a certain momentum, which is not taken account in the balance equation.
Thank you in advance.
Homework Statement
A rocket sled moves along a horizontal plane, and is retarded by a friction force friction = μW, where μ is constant and W is the weight of the sled. The sled’s initial mass is M, and its rocket engine expels mass at constant rate dM/dt ≡ γ; the expelled mass has constant...
Homework Statement
want to find the direction and moment of this diagram.
Homework Equations
The Attempt at a Solution
[/B]
I really do not have any idea about this question. So If someone helps, It'd be great.
Homework Statement
A projectile traveling vertically strikes a block and stays in it. The mass of the projectile is 0.20kg and its speed is 3.0m/s at the instant of impact. The mass of the block is 1.3kg. Air resistance may be neglected.
(a) How high does the block rise?
(b) How much kinetic...
1. Homework Equations
[/B]
P = mv The Attempt at a Solution
[/B]
VCos(30) + 0 = nCos(60) + 2Cos(20)
VSin(30) + 0 = nSin(60) + 2Sin(20)
where I let n = any speed,
I'm not sure if my attempt at the solution is correct.
Homework Statement
The luminosity of the star is defined as ##\phi = L/4\pi r^2##
The photons from the star hits the sail of mass ##M## and cross sectional area ##A##. What's the final velocity of the sail after getting hit by photons for a small time t? Assume the collision is elastic and the...
A pet mouse sleeps near the eastern edge of a stationary, horizontal turntable that is supported by a frictionless,
vertical axle through its center. The mouse wakes up and starts to walk north on the turntable. Is the momentum of the system constant?
i understand that the initial momentum is...
Homework Statement
it is given in the image i uploaded
Homework Equations
L→=r→ × p→[/B]
The Attempt at a Solution
If the angular momentum of a particle is the cross product of the position vector of the particle from the axis and its linear momentum, how can the angular momentum of m1 and...
There is something I don't quite understand about the law of conservation of angular momentum.
Let's say a person is rotating about an axis passing through his/her centre of mass, with an angular speed speed ω1, and has a rotational inertia I1 about about the centre of mass. No torque is acting...
Homework Statement
Assume two masses m1' and m2' are moving in the positive x-direction with velocities v1' and v2' as measured by an observer in S' before a collision. After the collision, the two masses stick together and move with velocity v' in S'. Show that if an observer in S' finds...