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A frame of reference that is accelerated with respect to an inertial frame of reference is called a non-inertial frame of reference. A coordinate system fixed on a circular disc rotating about a fixed axis with a constant angular velocity ω is an example of a non-inertial frame of reference. The relationship between the force →Frot experience by a particle of mass m moving on the rotating disc and the force →Fin experienced by the particle in an inertial frame of reference is
→Frot=→Fin+2m(→vrot×→ω)+m(→ω×→r)×→ω,
where →vrot is the velocity of the particle in the rotating frame of reference and →r is the position vector of the particle with respect to the centre of the disc. Now consider a smooth slot along a diameter of a disc of radius R rotating counterclockwise with a constant angular speed ω about its vertical axis through its center. We assign a coordinate system with the origin at the center of the disc, the x−axis along the slot, the y− axis perpendicular to the slot and the z− axis along the rotation axis →ω=ω→k. A small block of mass m is gently placed in the slot at →r=(R/2)→i at t=0 and is constrained to move only along the slot.
The net reaction of the disc on the block is