Law of Conservation of Angular Momentum - Artificial Satellite & Critical Velocity

The law of conservation of angular momentum states that the angular momentum about any axis of a given rotating body or a system of bodies is constant, if no external torque acts about that axis.

       L(total) = L1 + L2 + L3 + ........ = Constant

        The axis of rotation of an object will not change its orientation unless an external torque causes it to do so.

Rotational Kinetic Energy: 

        If a body is spinning about an axis with constant angular velocity, each point of the body is moving is a circular path and therefore has some K.E.

         To determine the total K.E of a spinning body we imagine it to be composed of tiny pieces. The rotational K.E of the whole body is the sum of the kinetic energies of all the parts.

       K.Erot = 1/2 I

Artificial Satellite: 

       Satellites are objects that orbit around the Earth. They are put into orbit by rockers and are held in orbits by the gravitational pull of the Earth. The low flying Earth satellites have acceleration 9.8 ms towards the center of the Earth. If they do not they would fly off in a straight line tangent to the Earth. When the satellite is moving  in a circle, it has an acceleration. In a  circular orbit around the Earth, the centripetal acceleration is supplied by gravity and we have g = v2/R.

Critical Velocity: 

        7.9 km s-1 is the minimum velocity necessary to put a satellite  into the orbit and called critical velocity.

        The higher the satellite, the slower will the required speed and longer it will take to complete one revolution around the Earth. Close orbiting satellites orbit the Earth at a height of about 400 km. Twenty four such satellites form the Global Positioning System.