A horizontal flat plate is free to rotate about a vertical axis through its centre, as shown in the figure below.
A small mass 
is placed on the plate, a distance 
from the axis of rotation. The speed of rotation of the plate is gradually increased from zero until the mass is seen to slide off the plate. The maximum frictional force 
between the plate and the mass is given by the expression:
where 
is the weight of the mass . The distance is 
. Determine the maximum number of revolutions of the plate per minute for the mass to remain on the plate. Explain your working.
