Coriolis Centrifugal Forces

The velocity and acceleration of an object relative to S in terms of the variables observed in rotating frame S’.

Multiplying eq. by mass m of the object, we get the following equation of motion:



interpreting above equation as the expression of Newton’s II law in rotating frame, F’ = m a’, we find the net force F’ on an object as seen from a rotating frame gets contribution from three sources, viz. (i) the ‘ordinary’ force F = m a, (ii) an inertial force called coriolis force, and (iii)another inertial force called centrifugal force. Both the inertial forces are in the direction perpendicular to axis of rotation hence X-Y plane.

The force is also an inertial force which arises if the frame S’ is rotating with angular acceleration   .

The centrifugal force depends only on the variable r’ (position) of the object and is always radially outwards:



= m ω² r’ e_r’                                                                                                                       (ii)

Its magnitude is equal to mω² r’, which is same as magnitude of ‘ordinary’ centripetal force acting on a particle moving in a circle of radius r’. Centrifugal force is an inertial force not seen in the stationary frame. It always acts on an object in a non-inertial rotating frame, whether the object is moving in a circle or otherwise.

The coriolis force depends on the velocity v’ of the object in the rotating frame and is always directed perpendicular to v’. If the object has no velocity in the rotating frame, no coriolis force acts on it. The effect of the coriolis force is to constantly deflect any moving particle from its instantaneous direction of motion (i.e. of v’) in a rotating frame.

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