Circular Motion

Formula for angle in radians

Angle(in radians) = arc length/Radius

Angular Velocity

The rate of change of angle with respect to time. (Angle/Time)

Relationship between linear speed (v), angular velocity(omega) and radius

V = r(omega)

To derive v=r(omega)

Centripetal Force

The force acting in towards the centre of a circle required to keep an object moving in a circle.

Centripetal Acceleration

If a body is moving in a circle the acceleration it has towards the centre is called centripetal acceleration.

Deriving the formulae for centripetal force

Relationship between periodic time and and angular velocity.

Time = 2(pi)/Angular velocity.

Relationship between periodic time and radius for a satellite in orbit.

T² = 4(pi)²R³/GM.

R = radius

G = gravitational constant

M = mass of the body being orbited

Derivation for periodic time of a satellite

Geostationary Satellite

A satellite which remain over a single position on earth (hence have the same periodic time)

Examples of Geostationary Satellites.