A cabin is rotating in a circular path of radius R with a uniform angular velocity , as shown in the figure. Inside the cabin, a table with a smooth horizontal surface is fixed. On the surface of this table, a smooth groove AB having length L ,( R) is constructed. This groove is oriented at an angle relative to the radius OA of the cabin's circular path. A small particle is initially placed at point A within the groo

Step-by-step solution

In the rotating frame of the cabin, the particle experiences a centrifugal force directed radially outward from the center of rotation O. At point A, the distance from the center O is R . The centrifugal force acting on the particle of mass m is F_c = m ^2 R , directed along the extended line OA. Since the length of the groove L R , the centrifugal force remains approximately constant in magnitude and direction as the particle moves from A to B. The groove AB is oriented at an angle with respect to the extended lin