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The planet Earth has three motions: it rotates about its axis, which gives us day and night; it revolves around the sun, giving us the seasons of the year, and through the Milky Way along with the rest of the Solar System. In each case, scientists have striven to calculate not only the time it takes, but the relative velocities involved. When it comes to the Earth rotating on its axis, a process which takes 23 hours, 56 minutes and 4.09 seconds, the process is known as a sidereal day, and the speed at which it moves is known as the Earth’s Angular Velocity. This applies equally to the Earth rotating around the axis of the Sun and the center of the Milky Way Galaxy.
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the 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, revolutions per second, etc. and is usually represented by the symbol omega (ω, rarely Ω). A radian, by definition, is a unit which connects the radius of an arc, the length of the arc and the angle subtended by the arc. A full radian is 360 degrees, hence we know that the Earth performs two radians when performing a full rotation around an axis. However, it is sometimes also called the rotational velocity and its magnitude – the rotational speed – is typically measured in cycles or rotations per unit time (e.g. revolutions per minute). In addition, when an object rotating about an axis, every point on the object has the same angular velocity.
Mathematically, the average angular velocity of an object can be represented by the following equation: ωaverage= Δθ/Δt, where ω is the radians/revolutions per second (on average), Δ is the change in quantity, θ is the velocity, and t is time. When calculating the angular velocity of the Earth as it completes a full rotation on its own axis (a solar day), this equation is represented as: ωavg = 2πrad/1day (86400 seconds), which works out to a moderate angular velocity of 7.2921159 × 10-5 radians/second. In the case of a Solar Year, where ωavg = 2πrad/1year (3.2×107 seconds), we see that the angular velocity works out to 2.0×10-7 rad/s.
We have written many articles about the angular velocity of Earth for Universe Today. Here’s an article about angular velocity, and here’s an article about why the Earth rotates.
If you’d like more info on angular velocity of Earth, check out the following articles:
Angular Speed of Earth
Earth’s Rotation
We’ve also recorded an episode of Astronomy Cast all about planet Earth. Listen here, Episode 51: Earth.
Sources:
http://en.wikipedia.org/wiki/Angular_velocity
http://hyperphysics.phy-astr.gsu.edu/hbase/rotq.html
http://hypertextbook.com/facts/2002/JasonAtkins.shtml
http://en.wikipedia.org/wiki/Earth%27s_rotation#Rotation_period
http://www.livephysics.com/tables-of-physical-data/mechanical/angular-speed-of-earth.html