A particle is undergoing circular motion in a horizontal circle, that lies within the smooth surface of a hemispherical bowl of radius 4r. Find the distance OC (explained in diagram) if the angular acceleration of the particle is equal to root (3g/8r).

Resolve the reaction force caused by the weight, mg, of the particle horizontally and vertically. Rsin(theta) = mg Rcos(theta)=m(CP)w^2 where w = root (3g/8r).thus tan(theta) = 8r/3CPconsider the right angled triangle OCP and find an expression for tan(theta) in terms of it's sides, hence tan(theta) = OC/CP. Thus, OC/CP = 8r/3CP and therefore Distance OC = 8r/3 (diagram and whiteboard working attached during interview)