Problem
Problem
A table with smooth horizontal surface is turning at an angular speed about its axis. A groove is made on the surface along a radius and a particle is gently placed inside the groove at a distance from the centre. Find the speed of the particle with respect to the table as its distance from the centre becomes .Intuitive explanation
The key is recognizing that in the rotating reference frame of the table, the particle experiences a centrifugal force pushing it outward along the groove—there's no friction to hold it back. You'll use energy conservation in this non-inertial frame: the centrifugal force does work as the particle slides from radius to , converting potential energy (in the rotating frame) into kinetic energy. Set up the work-energy equation carefully, accounting for how the centrifugal potential changes with distance from the axis.
Intuitive explanation
The key is recognizing that in the rotating reference frame of the table, the particle experiences a centrifugal force pushing it outward along the groove—there's no friction to hold it back. You'll use energy conservation in this non-inertial frame: the centrifugal force does work as the particle slides from radius to , converting potential energy (in the rotating frame) into kinetic energy. Set up the work-energy equation carefully, accounting for how the centrifugal potential changes with distance from the axis.