In
physics
,
angular frequency,
ω,
(also called the angular speed, radial frequency, and radian frequency) is a measure of rotation rate. A high rate of angular frequency means something is turning very fast. The angular frequency is the magnitude of the vector quantity angular velocity which is also known as angular frequency vector
.
Angular frequency is a measure of how fast an object is rotating. The
in the diagram should be
.
It is useful in many areas of maths and science as it allows understanding of many properties of physical objects in our world. In
SI
units, angular frequency is measured in
radians
per
second
, with dimensions t
?1
since radians are dimensionless.
Angular frequency is often given in radians per second (
) as it is easier to work with. In this way, the angular frequency is given by,
where
is the time (period) of a single rotation (revolution) and
is the frequency. This can be derived by considering
when
and
.
If a wheel turns by an angle
in a time
then the angular frequency at any moment is given by,
If the rotation speed is constant, this becomes,
and so it is similar to a speed.
For objects which are going in circles, the angular frequency may also be given as (in radians),
where
is the speed and
is the distance from the center of the circle.
This can be derived by considering
where
is the distance along the arc.
Thus
where
is the velocity.
The angular frequency is important in determining whether an object can stay above the ground against gravity, or whether a spinning top can stay standing. It also is important in creating the frequency of mains electricity supplies and reducing the heat due to friction in engines.
Objects are pulled towards the earth because of gravity. To oppose this, a satellite must go fast enough it misses the ground. For the forces to equal each other,
where
is the
mass
of the larger body and
is the
Gravitational constant
. To make a circle, the angular frequency must be equal to,
which leads to one of
Johannes Kepler
's Laws.
Generators in power stations rotate at some frequency. The speed at which these turn gives us the frequency that our electricity supplies are at. These can be slowed by large brakes or big heavy wheels which stop the generators from turning too quickly.
Name
|
Symbol
|
Definition
|
Radians per second
|
|
|
Revolutions per minute
|
|
|
Frequency per second
|
|
|
Degrees per second
|
|
|