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 ${\vec{F}}_{r o t}$ experienced by the particle of mass m moving on the rotating disc and the force $\vec{F_{i n}}$ experienced by the particle in an inertial frame of reference is ${\vec{F}}_{r o t} = \vec{F_{i n}} + 2 m ({\vec{v}}_{r o t} \times \vec{ω}) + m (\vec{ω} \times \vec{r}) \times \vec{ω}$ , where $\vec{v_{r o t}}$ is the velocity of the particle in the rotating frame of reference and $\vec{r}$ is the position vector of the particle with respect to the center of the disc
Now consider a smooth slot along a diameter of a disc of radius R rotating counter-clockwise 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 $(\vec{ω} = ω \hat{k})$ . A small block of mass m is gently placed in the slot at $\vec{r} = (R / 2) \hat{i}$ at $t = 0$ and is constrained to move only along the slot

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