The acoustic wave equation ( and the mass and momentum balance equations ) are often expressed in terms of a scalar potential where.

We make several assumptions to derive the momentum balance equation for an acoustic medium.

Then the balance of momentum reduces to

Different theories of the Circumpolar Current balance the momentum imparted by the winds in different ways.

When a body is acted upon by external contact forces, internal contact forces are then transmitted from point to point inside the body to balance their action, according to Newton's second law of motion of conservation of linear momentum and angular momentum ( for continuous bodies these laws are called the Euler's equations of motion ).

The behaviour of matter at the molecular scale including its density is determined by the balance between the electromagnetic force and the force generated by the exchange of momentum carried by the electrons themselves.

The animal relies on the forward and backward motions of its head and neck to maintain balance and the counter momentum while galloping.

Heraclius ' campaigns altered the balance, forcing the Persians on the defensive and allowing for the Byzantines to regain momentum.

On an upright bicycle, if a high gear is engaged, the rider may use one leg to gain minimal momentum and stand on the pedals and use his upper body to balance the bike ; this is not possible on a 2-wheeled recumbent bicycle.

This balance of momenta ensure that the momentum of the rifle / projectile / exhaust gas system is conserved without imparting much momentum ( recoil ) to the rifle itself.

Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of linear momentum and six infinitesimal strain-displacement relations.

Two sidewheels ( light aircraft tailwheels were used ) were manually lowered on stopping ; if the driver forgot and switched off the gyros and walked away, the car would continue to balance itself using the gyro momentum for a few minutes, and then the wheels would automatically be dropped to stop tipping.

Here the momentum of the current overcomes the vorticity balance holding the current to the topography and the current leaves the shelf.

However, using the computer systems in the locomotives, which communicate with each other, the engines are able to balance the momentum, preventing fuel waste.

This means that in order to unlock the wheel it must be turned backwards by a small amount, which is done by the return momentum of the balance wheel via the impulse pin ..

Because the momentum of the connecting rods alone in up and down motion is considerably less than that resulting from the combined horizontal movement of the connecting rods, piston and driving rod, a wheel counterweight cannot be made to balance the entire assembly perfectly during its complete rotation.

The velocity at which the surface then expands outwards is calculated and, from a basic Newtonian momentum balance, the velocity at which the rest of the tamper implodes inwards.

They quote about the same mass threshold as that of the U.S. apparatus, but a momentum threshold about 40 times greater.

The threshold mass is derived from the momentum threshold with the assumption of a mean impact velocity of Af in the U.S. work and Af in the U.S.S.R. work.

The mass scale used in Table 5-1 was derived on the assumption that the motion of the glowing trail is related to the momentum transfer to the trail by the meteorite, permitting the calculation of the mass if the velocity is known ( Cook and Whipple, 1958 ).

The propagation of sound waves in a fluid ( such as water ) can be modeled by an equation of motion ( conservation of momentum ) and an equation of continuity ( conservation of mass ).

The equation for the conservation of mass for an acoustic medium can also be derived in a manner similar to that used for the conservation of momentum.

The acoustic equations for the conservation of momentum and the conservation of mass are often expressed in time harmonic form ( at fixed frequency ).

Aerodynamics allows the definition and solution of equations for the conservation of mass, momentum, and energy in air.

The conservation of momentum equations are often called the Navier-Stokes equations, while others use the term for the system that includes conversation of mass, conservation of momentum, and conservation of energy.

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

If the path of the particle or centre of mass of the rigid body passes through the given origin, its angular momentum is zero.

It is very often convenient to consider the angular momentum of a collection of particles about their center of mass, since this simplifies the mathematics considerably.

The first term is just the angular momentum of the center of mass.

It is the same angular momentum one would obtain if there were just one particle of mass M moving at velocity V located at the center of mass.

The second term is the angular momentum that is the result of the particles moving relative to their center of mass.

Through the work of Werner Israel, Brandon Carter, and David Robinson the no-hair theorem emerged, stating that a stationary black hole solution is completely described by the three parameters of the Kerr – Newman metric ; mass, angular momentum, and electric charge.

The no-hair theorem states that, once it achieves a stable condition after formation, a black hole has only three independent physical properties: mass, charge, and angular momentum.

The simplest black holes have mass but neither electric charge nor angular momentum.

While the mass of a black hole can take any positive value, the charge and angular momentum are constrained by the mass.

Fundamental physical laws such as the conservation of mass, the conservation of momentum, and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through a constitutive relation.

Atomic orbitals are typically categorized by n, l, and m quantum numbers, which correspond to the electron's energy, angular momentum, and an angular momentum vector component, respectively.

The equations for the conservation of linear momentum for a fluid medium are

These assumptions and the resulting forms of the momentum equations are outlined below.

Additionally, if we assume that there are no viscous forces in the medium ( the bulk and shear viscosities are zero ), the momentum equation takes the form

In terms of components, these three equations for the conservation of momentum in cylindrical coordinates are

For example, the increase in rotational speed of a spinning figure skater as the skater's arms are contracted is a consequence of conservation of angular momentum.

As seen from the definition, the derived SI units of angular momentum are newton meter seconds ( N · m · s or kg · m < sup > 2 </ sup > s < sup >− 1 </ sup >) or joule seconds ( J · s ).

( The cross-product of velocity and momentum is zero, because these vectors are parallel.

Gyrobuses, which are powered by the momentum stored by a flywheel were tried in the 1940s.

For example, observable physical quantities are represented by self-adjoint operators, such as energy or momentum, whereas transformative processes are represented by unitary linear operators such as rotation or the progression of time.

In Planck units, the total electric charge Q and the total angular momentum J are expected to satisfy

Bonding can be described with three bonding electron pairs and two antibonding electrons, whose spins are aligned, such that the molecule has nonzero total angular momentum.

Most fuels, on the other hand, are in a singlet state, with paired spins and zero total angular momentum.

# Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.