The radial velocity varies inversely as the particle size -- a 1000-m-diameter particle near the orbit of Mars would reach the sun in about 60 million years.

where R < sub > i </ sub > is the position vector of particle i from the reference point, m < sub > i </ sub > is its mass, and V < sub > i </ sub > is its velocity.

If we define r < sub > i </ sub > as the displacement of particle i from the center of mass, and v < sub > i </ sub > as the velocity of particle i with respect to the center of mass, then we have

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 instantaneous position is a property of a particle, and its material derivative is the instantaneous velocity of the particle.

When the particle moves, its velocity is

where h is Planck's constant and p is the momentum of the particle ( mass × velocity for slow-moving particles ).

Nonbaryonic dark matter is classified in terms of the mass of the particle ( s ) that is assumed to make it up, and / or the typical velocity dispersion of those particles ( since more massive particles move more slowly ).

In the field of high-energy particle physics, the fundamental velocity unit is the speed of light c. Thus, dividing energy in eV by the speed of light in vacuum, one can describe the momentum of an electron in units of eV / c.

Under the special theory of relativity, a particle ( that has rest mass ) with subluminal velocity needs infinite energy to accelerate to the speed of light, although special relativity does not forbid the existence of particles that travel faster than light at all times ( tachyons ).

The red dot overtakes two green dots when moving from the left to the right of the figure. New waves seem to emerge at the back of a wave group, grow in amplitude until they are at the center of the group, and vanish at the wave group front. For surface gravity waves, the water particle velocities are much smaller than the phase velocity, in most cases.

where ' is the mass of the particle and v its velocity.

where m is the mass of the particle, c is the speed of light in a vacuum, is the Lorentz factor, and v is the velocity of the particle regardless of wave behavior.

Both in relativistic and non-relativistic quantum physics, we can identify the group velocity of a particle's wave function with the particle velocity.

Hyperbolas arise in practice in many ways: as the curve representing the function in the Cartesian plane, as the appearance of a circle viewed from within it, as the path followed by the shadow of the tip of a sundial, as the shape of an open orbit ( as distinct from a closed and hence elliptical orbit ), such as the orbit of a spacecraft during a gravity assisted swing-by of a planet or more generally any spacecraft exceeding the escape velocity of the nearest planet, as the path of a single-apparition comet ( one travelling too fast to ever return to the solar system ), as the scattering trajectory of a subatomic particle ( acted on by repulsive instead of attractive forces but the principle is the same ), and so on.

If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

Lorentz force f on a charged particle ( of electric charge | charge q ) in motion ( instantaneous velocity v ).

The force F acting on a particle of electric charge q with instantaneous velocity v, due to an external electric field E and magnetic field B, is given by:

They obtained a null result, and concluded that " there is no effect ... unless the velocity of the solar system in space is no more than about half that of the earth in its orbit ".

7 ), but " since the displacement is proportional to the square of the velocity " they concluded that the measured velocity was " probably less than one-sixth " of the expected velocity of the Earth's motion in orbit and " certainly less than one-fourth.

" Hence Galileo would have concluded that " falling bodies need not know anything if they all fall with the same velocity, unless interfered with by another force.

As no significant fringe shift was found ( corresponding to a velocity of 10 ± 10 km / s within the margin of error ), the experimenters concluded that time dilation occurs as predicted by Special relativity.

He concluded that the attraction is proportional to, where S is earth's molecular surface area, v is the velocity of the particles, and ρ is the density of the medium.

While Sagnac himself concluded that his theory confirmed the theory of an aether at rest, Laue's earlier calculation showed that it is compatible with special relativity as well because in both theories the speed of light is independent of the velocity of the source.

When the results of this theory were compared with the quantity of water actually discharged, Newton concluded that the velocity with which the water issued from the orifice was equal to that which a falling body would receive by descending through half the height of water in the reservoir.

He concluded that the birds, mostly juveniles and local migrants, are disturbed by high velocity winds at their roost.

Additionally, PWM ( pulse-width modulation ) anemometers are also used, wherein the velocity is inferred by the time length of a repeating pulse of current that brings the wire up to a specified resistance and then stops until a threshold " floor " is reached, at which time the pulse is sent again.

If the vector field represents the flow velocity of a moving fluid, then the curl is the circulation density of the fluid.

It measures the amount of " stuff " flowing through a surface per unit time in a " stuff fluid " of density moving with local velocity F. Its exterior derivative is then given by

If ω is directly proportional to k, then the group velocity is exactly equal to the phase velocity.

If the waves are propagating through an anisotropic ( i. e., not rotationally symmetric ) medium, for example a crystal, then the phase velocity vector and group velocity vector may point in different directions.

If the bullets have to travel a varying distance from the case to the point where they engage the rifling, then this can result in variations in pressure and velocity.

A positively charged particle will be accelerated in the same linear orientation as the E field, but will curve perpendicularly to both the instantaneous velocity vector v and the B field according to the right-hand rule ( in detail, if the thumb of the right hand points along v and the index finger along B, then the middle finger points along F ).

In SI units, if the mass is in kilograms and the velocity in meters per second, then the momentum is in kilograms meters / second ( kg m / s ).

If, e. g., u is the speed of a particle, then the straightforward notation for its velocity is u, < u > u </ u >, or.

0, then the optimal runner speed will be u = V < sub > i </ sub > / 2, or half the initial jet velocity.

When the speed of the runner is equal to the initial jet velocity, the torque is zero ( i. e. when u = V < sub > i </ sub >, then T = 0 ).

The increased velocity meant that new problems arrived, and so bullets went from being soft lead to harder lead, then to copper jacketed, in order to better engage the spiraled grooves without " stripping " them in the same way that a screw or bolt thread would be stripped if subjected to extreme forces.

In it he states, "[...] the early discovery that the great Andromeda spiral had the quite exceptional velocity of – 300 km (/ s ) showed the means then available, capable of investigating not only the spectra of the spirals but their velocities as well.

A net restoring force then tends to slow it down, until its velocity vanishes, whereby it will attempt to reach equilibrium position again.

If an object moves with angular velocity ω around a circle of radius r centered at the origin of the x-y plane, then its motion along each coordinate is simple harmonic motion with amplitude r and angular frequency ω.

When ω is the angular velocity of the turbine, then the blade speed is.

After moving in that direction to another nearby point, one's velocity would then be given by a vector in the tangent space of that nearby point — a different tangent space, not shown.

This yields a net space velocity of :</ ref > This result can then be used to compute an orbital path of Tau Ceti through the Milky Way galaxy.

For example, if v consists of the x, y, and z-components of velocity, then v is a contravariant vector: if the coordinates of space are stretched, rotated, or twisted, then the components of the velocity transform in the same way.