Theory of Relativity (Non-inertial frame and Fictitious forces) Lecture-3

Theory of Relativity

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3.Non-inertial frame and Fictitious forces : A football is kept in a stationary bus and we can find that it would at rest. If the bus starts moving, we will find the ball moving from its initial position without applying any external force by the way of interaction with other objects. The above movement is as a result of accelerating frame (bus). Any frame that is found to accelerate is called non inertial frame. Here, Newton's second law 'f = ma ' cannot be used without accounting for additional force acting on the object due to accelerated frame. We turn our attention to appearance of physical laws to an observer in a system accelerating at rate  with respect to, inertial system.                     By rewriting the acceleration relation, we derived earlier (eq.1.3)                            .............................................................. ( 1.5 ) where  is the acceleration of primed coordinate system. By multiplying the mass of the body, 'm' we get                                          or         ................................................... ( 2 )    Here  is the true force due to the physical interaction, is the force due to physical interactions observed in the primed coordinate system (apparent force) and  is the fictitious force.