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A solid cylinder and ring are released from rest at the top of an inclined plane. Find the ratio (𝑣_𝑐𝑦𝑙/𝑣_𝑟𝑖𝑛𝑔 ) of their velocities when they reach the bottom, assuming pure rolling. A solid cylinder starts rolling down on an inclined plane from its top and v is velocity of its center of mass on reaching the bottom of inclined plane. If a block starts sliding down on an identical inclined plane but smooth, from its top, then the velocity of the block on reaching the bottom of inclined plane is Calculate the ratio (𝑡_𝑠𝑝ℎ𝑒𝑟𝑒:𝑡_𝑐𝑦𝑙) of the times taken by a uniform solid sphere and a solid cylinder of the same mass and the same radius to roll down through the same distance from rest on an inclined plane. The thin uniform rod of mass M = 1 kg shown in the figure below has length L = 2 m and can pivot in a vertical plane about a frictionless pin through one end. If the tangential speed of the end of the rod as it passes through the horizontal position is 7 m/s, from what initial angle θ was it released?