What is Momentum balance: Definition and 14 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





{\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. E

    How Is Angular Momentum Calculated Without Considering Gravity and Viscosity?

    we neglect gravity and viscosity efects i really can't understand how does the author managed to get the equation in the image
  2. A

    Control volume and the momentum theorem

    I'm studying fluid and propulsion mechanics by myself. I stumbled upon this website from MIT: http://web.mit.edu/16.unified/www/SPRING/propulsion/UnifiedPropulsion2/UnifiedPropulsion2.htm#fallingblock It states that "Newton’s second law for a control volume of fixed mass" is $$\sum...
  3. yash_it_is

    Gauge pressure in Momentum conservation of fluids.

    I want to ask why is it that we use gauge pressure instead of absolute pressure in CV analysis for momentum conservation of fluids. I did read that because P(atm) would be present everywhere so it won't have a net effect on the CV but it's highly non intuitive as I can't apply force balance on...
  4. Henrique Orlandini

    Terminal velocity of a skier using a Momentum Balance

    Homework Statement [/B] A skier (mass M = 100 kg) going down a slope with inclination θ = 30°, sliding in a fluid-like snow (viscosity μ = 100 mPa*s) of thickness h = 0.01 m, using a pair of skis, each one with a surface area of As = 0.15 m2, reaches terminal velocity vt after some distance...
  5. T

    Block sliding down hill splits into two blocks

    I am currently working on this problem and I am stuck as to how to approach or solve it. The problem is that a block of mass 11000kg is sliding down a slope with a height of 1000m, angle of 40 degrees and the coefficient of friction between the block and the slope is 0.1. The block splits...
  6. B

    Terminal velocity of a raindrop

    Homework Statement A raindrop of initial Mass ##M_0## starts to fall from rest under the influence of gravity. Assume that the drop gains mass from the cloud at a rate proportional to the product of its instantaneous mass and its instantaneous velocity ##\dfrac{dM}{dt} = kMV##, where ##k## is...
  7. W

    Understanding Fluid Flow and Stress in Two Dimensions with LaTex Tutorial

    Homework Statement Homework Equations 0=viscous+gravitational+pressure I saw in the solutions that pressure=0 in this case, but why? I also knew that : accumulation= flow in - flow out+generation, why not use this one? The Attempt at a Solution (their solution) We are interested in...
  8. M

    Unsteady Pipe-Flow Momentum Balance: Solving for Volumetric Time Rate of Change

    Hi PF! Suppose we have an incompressible UNSTEADY fluid passing through a level pipe. Let station 1 have area, velocity, and pressure ##A_1##, ##V_1(t)## and ##P_1(t)##. Station 2 is defined similarly. I know the unsteady Bernoulli equation could solve this, but if I wanted to make a momentum...
  9. T

    Is Conservation of Energy the Key to Solving This Tricky Problem?

    I find this problem kind of tricky. I think it must be a, since a change in momentum of the car causes the same change in momentum of the earth.
  10. MexChemE

    Shell balances in cylindrical coordinates

    Hello, PF! I have some doubts about setting up shell balances in a cylindrical geometry. Consider a fluid flowing down a vertical pipe. In order to perform the momentum balance, we take a cylindrical (annular) shell of length L and width Δr. The analysis of such system can be found in chapter 2...
  11. C

    What Is the Correct Equation for Fluids Momentum Balance?

    Homework Statement Attached document Homework Equations m(flow)*(v1-v2)+P1A1-P2A2 The Attempt at a Solution I did a mass balance to plug into the momentum balance, but I am not getting the final equation correct.
  12. F

    Momentum balance derivation in equations

    I'm a little confused, in my fluid mechanics course we've covered many equations and they are all derived using an x-direction fluid flow. If I was to use these in a system in which fluid flowed in the y-direction would I have to re-derive them? Or would it be more of a case of using a...
  13. A

    (Fluid Flow) Differential momentum balance problem

    Attached pdf contains the problem, and my progress in working it. My question is, I'm not really sure how to proceed. Anyone care to push me in the right direction?
  14. A

    Fluid flow problem with the momentum balance equation

    All problem info, and my work is done in the attached pdf. Basically, I'm not sure that I have done it correctly.