# conservation of momentum Definition and Topics - 122 Discussions

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.

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1. ### Hinged rod rotating, falling and hitting a mass

Assuming no friction anywhere, no drag and perfect inelastic collision Using conservation of mechanical energy i can determine the rotational speed of the rod right before collision occurs. mgh=1/2*i*w^2 center of mass falls 1/2*L so we have: M*g*1/2*L = 1/2*(1/3*M*L^2)*w^2 Solving for w...
2. ### Amplitude of oscillation of a mass which is the pivot of a pendulum

1) By conservation of mechanical energy we have ##m_2gl(1-\cos(\alpha))+m_1gl=\frac{1}{2}m_1v_1^2+\frac{1}{2}m_2v_2^2+m_1gl## and by conservation of linear momentum along the x-axis we have ##m_1v_1+m_2v_2=0## which gives us ##v_2=\sqrt{\frac{2m_1gl(1-\cos(\theta))}{m_1+m_2}}## and...
3. ### Stopping a Bullet

(a) ##u_{min}=\big(1+\frac{m_2}{m_1}\big)\sqrt{2\mu_k g d}## (b) ##x_f=\sqrt{\frac{2h}{g}\Big(\big(\frac{m_1}{m_1+m_2}u\big)^2-2\mu_k g d\Big)}## Can someone check please?
4. ### Disk hit by two masses

1) By conservation of linear momentum: ##m_1 v_1-m_2v_2=(m+m_1+m_2)v_{cm}\Rightarrow v_{cm}=\frac{m_1}{m+m_1+m_2}v_1-\frac{m_2}{m+m_1+m_2}v_2=\frac{3}{8}\frac{m}{s}##; 2) By conservation of angular momentum: ##-Rm_1v_1-Rm_2v_2=I_{total}\omega=(I_{disk}+m_1R^2+m_2R^2)\omega## so...
5. ### Conservation of momentum in an oblique launch and projectile explosion

This problem I already solved using another resource (just get the coordinate of the center of mass reach and from it, get to the larger mass. R = (3v02) / (4g)). But I'm having some trouble calculating using moment conservation. Here what I've done so far: $$3\vec v_0 = \vec v_1 +2\vec v_2$$...
6. ### Conservation of momentum problem (from "200 Puzzling Physics Problems")

My proposed solution: When the student stops at the end, suppose the carriage is moving at speed u. 0 = (M+2m)u - m(v - u) ==> u = mv/ M+3m After jumping out, the total momentum of the Carriage + collector system is 0 - mu = -m^2v/ M+3m. By conservation of momentum for the Carriage +...
7. ### Conservation of energy in Gravitation

Suppose a rocket is moving at radial velocity vr and tangential velocity vt in the Sun's gravitational field. At some time, the rocket enters the gravitational field of Mars (with the above mentioned velocities), and gravitation effects due to the Sun can be ignored. After more time, the rocket...
8. ### Velocity of a cart moving in the rain as a function of time

At time t = 0, the mass of the cart is ##M_0## and velocity is ##v_0## in a time interval ##dt## let a mass of ##dm## be added to the cart due to the pouring water and let the reduction in speed be ##dv## ##\lambda = dm/dt## applying conservation of momentum from the ground frame gives M_0...
9. ### Conservation of angular momentum and its counterpart for linear momentum

Hi, I have just joined the forum. Thank you all for being a part of such places so that people like me can get answers to the questions on their minds! --------------------------- I have been trying to understand how a quadcopter yaws. Referring to the figure below which is bird's eye view of...
10. ### Cars Collide on a Hill, Conservation of Momentum Help Please

QUESTION: ----------- For the purposes of this problem, we will define the direction of Vehicle A's initial velocity as the positive direction: While driving on a road that is inclined at an angle of 10 degrees above the horizontal, Vehicle A and Vehicle B are in a head-on collision lasting...
11. ### Determining position of an object after inelastic collision

Homework Statement A 39,000 lb truck A and a 3968 lb sports car B collide at an intersection. At the moment of the collision, the truck and the sports car are traveling with speeds vA = 70 mph and vB = 30 mph. Assume that the entire intersection forms a horizontal surface. Letting the line of...
12. ### Ballistocardiograph and conservation of momentum

Hi, once again I'm probably asking a question that is more about human physiology than physics (I recently asked a question that had to do with hearing). I found a (definitely too hasty) reference to a ballistocardiograph in a high school textbook. So I got curious about the way this apparatus...
13. ### Conservation of Momentum (Explosion Kinematics)

Homework Statement [/B] A 3200 kg space vehicle (including a launchable lifeboat) is travelling with a velocity of 300 m/s in a straight trajectory [East]. The lifeboat (200 kg) is fired at a speed of 1000 m/s [N of original trajectory]. a) After firing it is found that the horizontal...
14. ### Final velocities of two objects in a 2D elastic collision

Homework Statement An atomic nucleous of mass m travelling with speed v collides elastically with a target particle of mass 3.0m (initially at rest) and is scattered at 45o (a). What are the final speeds of the two particles? Advice: eliminate the target particle's recoil angle by...
15. ### Four men jumping from a raft

Suppose four men are on a square shaped raft.All have jumped mutually perpendicularly into the river from the raft at velocity 2m/s at the same time. What will be the velocity of the center of mass of the raft? The implied assumption is likely that the mass of the four men is same. I think the...
16. ### Simple Ice Skater with Conservation of Angular Momentum

Homework Statement Not a HW problem, but a "me re-thinking things" problem. Please tell me where my thinking is flawed: You have an ice skater with no net external torques acting on him/her. (We are analyzing the time after they have to get an external torque on them by pushing off of the...
17. ### Four friends jump from a raft

Homework Statement Suppose your three friends and you are on a square shaped raft. You all have jumped mutually perpendicularly into the river from the raft at velocity 2m/s at the same time. What will be the velocity of the center of mass of the raft? Homework Equations Maybe,the law of...
18. ### Maximizing rocket velocity - shoot fuel at once, or slowly?

I stumbled upon a 3-year old article from Wired that poses this question on rockets: Suppose I have two rockets with a mass M and fuel mass m. Rocket A shoots all the fuel at once (again, like a nuclear propulsion engine) with a fuel speed of u and rocket B shoots two blobs of fuel—first a shot...
19. J

### D’Alambert vs Newton’s second law?

I’m a bit stuck with differentiating between the conservation of energy and D’Alambert. For a question I need to find the average resistance of the ground after it has been struck by an object. I chose to look at the equation as Ma + Mgh - Fr = 0. Can you advise if this is correct?
20. ### How do we know how long the force is acting on an object?

Hey all, so I'm self studying and I came across this question: A ## 2 kg ## cart, traveling on a horizontal air track with a speed of ## 3 m/s##, collides with a stationary ##4 kg## cart. The carts stick together. The impulse exerted by one cart on the other has a magnitude of: A. ## 0 ## B...
21. ### Momentum transfer from linear to angular motion

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...
22. A

### Elastic Collision Angle Proof

Homework Statement Prove that in the elastic collision of two objects of identical mass, with one being a target initially at rest, the angle between their final velocity vectors is always 90 degrees. Homework Equations m1v1+m2v2 = m1v1'+m2v2' 1/2m1v1^2 +1/2m2v2^2 = 1/2m1v1'^2 + 1/2m2v2'^2...
23. A

### Elastic collision heavy particle problem

Homework Statement Suppose a heavy particle (mass m1) has an elastic head-on collision with a very light particle of mass m2 initially at rest. Show that if m1>>m2, the velocity of the projectile (m1) is practically unchanged, whereas the target particle (m2) acquires a velocity v2' = 2v1...
24. T

### Confusion with "explosive" part, Conservation of Momentum

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...
25. ### Conservation of linear momentum in this system

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...
26. B

### Conservation of Angular Momentum of Train on Disk

Homework Statement A horizontal plywood disk with mass 6.90 kg and diameter 1.14 m pivots on frictionless bearings about a vertical axis through its center. You attach a circular model-railroad track of negligible mass and average diameter 1.04 m to the disk. A 1.40 −kg , battery-driven model...
27. J

### Final speed and direction after a collision (elastic+inelastic)

Homework Statement A billiard ball moves at a speed of 4.00 m/s and collides ELASTICALLY with an identical stationary ball. As a result, the stationary ball flies away at a speed of 1.69 m/s. Determine a. the final speed and direction of the incoming ball after the collision b. the direction...
28. J

### Find speed and direction of a particle after collision

SOLVED THANK YOU
29. S

### Conservation of Work/Momentum of Puck Sliding Off Plate

Homework Statement I saw this problem from a few years ago here on Physics Forum (https://www.physicsforums.com/threads/work-energy-theorem-problem.823990/) and wanted some clarification. Here is the problem: A curved plate of mass M is placed on the horizontal, frictionless plane as shown...
30. ### Kinetic theory of gases: rebound speed and force questions

Hi everyone, I remember years ago at school memorising the derivation of the formula for pressure in the kinetic theory of gases, as explained in this Youtube video: Thinking a little more deeply about this derivation there are two things I don't get: 1) At 0:53, the video says the molecule...