A small ring with a mass of 
can slide frictionlessly along a wire which is twisted into a semicircular loop with radius 
as shown in the figure below. The semicircular loop is rotated around an axis at an angular velocity 
.
Figure 1: Rotating semicircular loop with ring
Draw the external forces on the ring when the ring is at the height of 
with respect to the lowest position, and name the forces.
Find the relationship between the angular velocity and the height .
At what angular velocity is the ring at the height of 
?
What is the resultant force acting on the ring?
What force does the semicircular loop exert on the ring?
Explain whether it is possible for the ring to fall off the rotating loop!
with which the loop acts perpendicular to the ring and has a direction towards the centre of the loop with radius 
,
of the ring.
.
.
