Everything about Angular Velocity totally explained
» Do not confuse with angular frequency
In
physics, the
angular velocity is a
vector quantity (more precisely, a
pseudovector) which specifies the
angular speed, and axis about which an object is rotating. The
SI unit of angular velocity is
radians per second, although it may be measured in other units such as degrees per second, degrees per hour, etc. When measured in cycles or rotations per unit time (for example
revolutions per minute), it's often called the rotational velocity and its magnitude the
rotational speed. Angular velocity is usually represented by the symbol
omega (
Ω or
ω). The direction of the angular velocity vector is perpendicular to the plane of rotation, in a direction which is usually specified by the
right hand rule.
The angular velocity of a particle
Two dimensions
The angular velocity of a particle in a 2-dimensional plane is the easiest to understand. As shown in the figure on the right (typically expressing the angular measures φ and θ in
radians), if we draw a line from the origin (O) to the particle (P), then the velocity vector (
It can be seen that the velocity of a point in a rigid body can be divided into two terms - the velocity of a reference point fixed in the rigid body plus the cross product term involving the angular velocity of the particle with respect to the reference point. This angular velocity is the "spin" angular velocity of the rigid body as opposed to the angular velocity of the reference point O' about the origin O.
It is an
important point that the spin angular velocity of every particle in the rigid body is the same, and that the spin angular velocity is independent of the choice of the origin of the rigid body system or of the lab system. In other words, it's a physically real quantity which is a property of the rigid body, independent of one's choice of coordinate system. The angular velocity of the reference point about the origin of the lab frame will, however, depend on these choices of coordinate system. It is often convenient to choose the
center of mass of the rigid body as the origin of the rigid body system, since a considerable mathematical simplification occurs in the expression for the
angular momentum of the rigid body.
Further Information
Get more info on 'Angular Velocity'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://angular_velocity.totallyexplained.com">Angular velocity Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
