Acockroach crawls with constant speed in a circular path of radius b on a phonograph turntable rotating with constant angular speed omega. the circle path is concentric with the center of the turntable. if the mass of the insect is m and the coefficient of static friction with the surface is the table is mu sub s, how fast, relative to the turntable, can the cockroach crawl before it starts to slip if it goes (a) in the direction of rotation and (b) opposite to the direction of rotation?