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URGENT!! a) A ball of radius ? and mass ? is rolling without slipping on the...

URGENT!!

a) A ball of radius ? and mass ? is rolling without slipping on the surface of a ring of radius ?. At a given instant, the ring is rotating with angular speed Ω counterclockwise as shown in the figure and the ball is rolling without slipping. What is the speed of the center of mass of the ball at that instant if it has clockwise angular speed of ω?

b)A yo-yo of mass ? has a spool of radius ? and an axle of radius of ?/2 (see the image below). Its moment of inertia about an axis passing through the center of the yo-yo can be approximated by ?0 = 1 2 ?? 2 . The yo-yo is placed on a horizontal surface, and the string is pulled with a force of magnitude ? in the direction shown in the figure. The axis of rotation of the yo-yo is perpendicular to the page. The downward acceleration of gravity is g. The coefficient of static friction between the yo-yo and the surface is ?? . What is the maximum magnitude of the pulling force, F, for which the yo-yo will roll without slipping?

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