I am trying to digest the following problem.
Suppose a block of mass $m$ lying on a horizontal, frictionless turntable is connected to a string attached to the center of the turntable, as shown in figure below. According to an inertial observer, if the block rotates uniformly, it undergoes an acceleration of magnitude $\frac{v^2}{r}$, where $v$ is its linear speed. The inertial observer concludes that this centripetal acceleration is provided by the force $T$ exerted by the string and writes Newton’s second law as $T = mv^2/r$.
In my opinion, the box cannot move in circular motion because there is no friction between the table and the box. Instead, the box will slip so it will stay at the same position.
Can a box on a frictionless rotating table rotate?