The carnival and fairground ride called "The Rotor" or "The Barrel" is a popular example in physics textbooks. Suppose such a ride has been designed so that the maximum force of static friction between riders and the carpeted wall is just sufficient to support the riders when it has radius R and turns at angular speed ω. R If the fair owner wants a new version of the ride that has twice the radius, but is otherwise similar, what new angular speed ω ′ would be needed for the new ride?A pulley that has a moment of inertia 3 4 M R2 and radius R rotates about an axis through its center. A string is wrapped around the disk and exerts a constant force 1 2 M g tangential to the disk. Find the tangential acceleration of a point on the rim of the disk.