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A uniform solid disk of radius R and mass M is free to rotate on a frictionless pivot through a point on its rim, as shown below. The disk is released from rest in the position shown by the copper-colored circle. What is the speed of the lowest point on the disk in the dashed position? A solid cylinder rolls down an inclined plane of height 3 m and reaches the bottom of the plane with angular speed of 2√2 rad/s. The radius of the cylinder must be [Take g = 10 m/s2] A hollow sphere with mass M and radius R rolls without slipping down a slope that makes an angle of θ = 35o with the horizontal. The angular acceleration of the sphere is 4 rad/s2, and the coefficient of static friction between the slope and sphere surfaces is μs = 0.2. Calculate the radius of the sphere.