In physics, angular momentum, moment of momentum, or rotational momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis.

For a rigid body rotating around an axis of symmetry ( e. g. the blades of a ceiling fan ), the angular momentum can be expressed as the product of the body's moment of inertia, I, ( i. e. a measure of an object's resistance to changes in its rotation rate ) and its angular velocity ω:

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:

where I is the moment of inertia of the object ( in general, a tensor quantity ), and ω is the angular velocity.

This second term can be even further simplified if the particles form a rigid body, in which case it is the product of moment of inertia and angular velocity of the spinning motion ( as above ).

the angular momentum is expressed as the product of the moment of inertia of the object and its angular

where I is the moment of inertia of the object ( in general, a tensor quantity ) and ω is the angular velocity.

Sometime this may not be possible, in these cases the angular momentum component along the axis of rotation is the product of angular velocity and moment of inertia about the given axis of rotation.

A spinning figure skater reduces her moment of inertia by pulling in her arms, causing her rotation rate to increase.

By bringing part of mass of her body closer to the axis she decreases her body's moment of inertia.

Angular momenta of a classical object .< p > Left: intrinsic " spin " angular momentum S is really orbital angular momentum of the object at every point ,</ p >< p > right: extrinsic orbital angular momentum L about an axis ,</ p >< p > top: the moment of inertia tensor | moment of inertia tensor I and angular velocity ω ( L is not always parallel to ω )</ p >< p > bottom: momentum p and it's radial position r from the axis .</ p > The total angular momentum ( spin + orbital ) is J.

:: is the moment of inertia of the molecule

Also, for a diatomic molecule the moment of inertia is

So, substituting the angular momentum and moment of inertia into E < sub > rot </ sub >, the rotational energy levels of a diatomic molecule are given by:

:: angular momentum = rotational velocity × moment of inertia,

Using this and the known moment of inertia of the flywheel, the computer is able to calculate speed, power, distance and energy usage.

The energy dissipated can be accurately calculated given the known moment of inertia of the flywheel and a tachometer to measure the deceleration of the flywheel.

In angular mechanics, torque is analogous to the Newtonian mechanics parameter of force, moment of inertia to mass, and angle to distance.

The increased moment of inertia makes the long gun slower and more difficult to traverse and elevate, and it is thus slower and more difficult to adjust the aim.

Since it has only a tiny fraction of its parent's radius ( and therefore its moment of inertia is sharply reduced ), a neutron star is formed with very high rotation speed, and then gradually slows down.

Therefore, it will have to be constant in the external reference frame, but the moment of inertia tensor ( I ) is non-constant in this frame because of the lack of symmetry.

He will not curb his instinctual desires but release the energy within him that makes him feel truly and fully alive, even if it is only for this brief moment before the apocalypse of annihilation explodes on earth.

For the present it is enough to note that in the grotesque figure of Jacoby, at the moment of his collapse, all these elements come together in prophetic parody.

Indeed, it is probable that this point is reached the moment the third level of change begins.

This happens at the moment man loses the perception of moral substance in himself, of a nature that, in Maritain's words, is perceived as a `` locus of intelligible necessities ''.

If we remove ourselves for a moment from our time and our infatuation with mental disease, isn't there something absurd about a hero in a novel who is defeated by his infantile neurosis??

it is a dedication which began the moment she met Carl.

Not for a moment do we forget that our own fate is firmly fastened to that of these countries ; ;

An idea, of the sort that we have in mind, although of necessity readily available to imagination, is more general in connotation than most poetic or literary images, especially those appearing in lyric poems that seek to capture a moment of personal experience.

Since Laos is of no more purely military value to Moscow itself than it is to Washington, this approach might be expected to head off Mr. Khrushchev for the moment.

If they do meet and recognize one another, slap backs and embrace, the moment soon is done.

The moment of truth is the moment of crisis.

Too often it is thought of at the last moment of new product introduction.

The number depends on who is talking at the moment.

`` I paint the nothing '', he said once to Franz Kline and myself, `` the nothing that is behind the something, the inexpressible, unpaintable ' tick ' in the unconscious, the ' spirit ' of the moment resting forever, suspended like a huge balloon, in non-time ''.

The general theory of resonance shifts is used to derive a general expression for the second moment Af of a polycrystalline paramagnetic sample and is specialized to Af.

Field shifts were derived from the mean value of the resonance line, defined as the field about which the first moment is zero.

But it is true that the therapist can sense, when he hears this stereotype, that there are at this moment many emotional determinants at work in it, a blurred babel of indistinct voices which have yet to become clearly delineated from one another.

But when to represents to consciousness in that was the moment that I came to, and similarly in that was the moment I came to, there is much stronger stress on to.

But to say that at a moment in history something is new is not necessarily to say that it is modern ; ;

The moment magnitude is the most common scale on which earthquakes larger than approximately 5 are reported for the entire globe.

It is fitting that at this solemn moment we take the pledge of dedication to the service of India and her people and to the still larger cause of humanity.

This explains why superparamagnetic nanoparticles have a much larger susceptibility than standard paramagnets: they behave exactly as a paramagnet with a huge magnetic moment.

The formulation "... that willing suspension of disbelief for the moment which constitutes poetic faith ," of necessity implies that there are different sorts of suspension of disbelief and specifies that poetic faith is one instance of a larger class.

The count claimed to have the most powerful army and at any moment could defeat the Hashshashin, as its army was 10 times larger.

Furthermore, neither side had deployed the ships which they both held in reserve, of which the Danish reserve was arguably the larger, and the truce effectually prevented this deployment at a moment where the British fleet was exposed.

So the bicycle wheel has a larger moment of inertia than the baby buggy wheel.

At the moment that the compressor hose attached to actor Tatsuya Nakadai was activated it blew a coupling causing a much larger gush of fluid than planned.

Surfers generally find a shortboard very quick to maneuver compared with other types of surfboards, but because of a lack of flotation due to the smaller size, harder to catch waves with, often requiring steeper, larger and more powerful waves and very late takeoffs, where the surfer catches the wave at the critical moment before it breaks.

A second, larger flag was run up in its place, and this second flag-raising was the moment captured by Associated Press photographer Joe Rosenthal in his famous photograph.

As time progresses forward, the future light cone of a given event will eventually grow to encompass more and more locations ( in other words, the 3D sphere that represents the cross-section of the 4D light cone at a particular moment in time becomes larger at later times ).

At the moment, orisun. com and the-sun. com. hk are still trying to struggle for a larger market share as more and more newspapers and newsmagazines are having their online versions.

Although it's true I had thought it would have been better to put a larger engine, the moment I drove the Honda NSX, all the benchmark cars — Ferrari, Porsche, Lamborghini — I had been using as references in the development of my car vanished from my mind.

* In structural engineering, κ is the ratio of the smaller factored moment to the larger factored moment and is used to calculate the critical elastic moment of an unbraced steel member.

This ringfort which is overlooked and in close proximity to another larger ringfort, Garryduff I, has provided archaeologists with no evidence of habitation or settlement, and the pre-eminent theory at the moment is that this ringfort was possibly used as an enclosure for livestock.

A larger moment arm reduces the force needed to rotate a pulley.

Here he produced novel work on the diffraction of atoms ( using crystal surfaces ) and also proved that the magnetic moment of the proton was much larger than had been previously supposed.

Not only do larger gears occupy more space, the mass and rotational inertia ( moment of inertia ) of a gear is proportional to the square of its radius.

The larger the distance between the center of gravity and the center of pressure, the greater the moment arm on the restoring torque.

From this moment onwards, computers can only be made more powerful if they are made larger in size.

At that moment, Gosha finds out that Katerina is a factory director and realizes that her salary must be larger than his own.

It was this moment, and this poignant mix of defeat, heroic self-sacrifice, and willingness to face imminent death that Rodin captured in his sculpture, scaled somewhat larger than life.