Question

4. How is angular velocity represented vectorially ?
​

Answer 1

In physics, angular velocity ({\displaystyle {\vec {\omega }}} or {\displaystyle {\vec {\Omega }}}), also known as angular frequency vector,[1] is a vector measure of rotation rate, that refers to how fast an object rotates or revolves relative to another point, i.e. how fast the angular position or orientation of an object changes with time.

Angular velocity

Common symbols

ωIn SI base unitss−1Extensive?yesIntensive?yes (for rigid body only)Conserved?no

Behaviour under

coord transformation

pseudovector

Derivations from

other quantities

There are two types of angular velocity: orbital angular velocity and spin angular velocity. Spin angular velocity refers to how fast a rigid body rotates with respect to its centre of rotation. Orbital angular velocity refers to how fast a point object revolves about a fixed origin, i.e. the time rate of change of its angular position relative to the origin. Spin angular velocity is independent of the choice of origin, in contrast to orbital angular velocity which depends on the choice of origin.

In general, angular velocity is measured in angle per unit time, e.g. radians per second (angle replacing distance from linear velocity with time in common). The SI unit of angular velocity is expressed as radians per second with the radian having a dimensionless value of unity, thus the SI units of angular velocity are listed as 1/s or s−1. Angular velocity is usually represented by the symbol omega (ω, sometimes Ω). By convention, positive angular velocity indicates counter-clockwise rotation, while negative is clockwise.

For example, a geostationary satellite completes one orbit per day above the equator, or 360 degrees per 24 hours, and has angular velocity ω = (360°)/(24 h) = 15°/h, or (2π rad)/(24 h) ≈ 0.26 rad/h. If angle is measured in radians, the linear velocity is the radius times the angular velocity, {\displaystyle v=r\omega }. With orbital radius 42,000 km from the earth's center, the satellite's speed through space is thus v = 42,000 km × 0.26/h ≈ 11,000 km/h. The angular velocity is positive since the satellite travels eastward with the Earth's rotation (counter-clockwise from above the north pole.)