A Physics professor is experimenting with a solid cylinder attached to a rod that passes through the center of mass of the cylinder and is perpendicular to its flat surfaces. She holds the cylinder by the rod in the air and sets it with angular speed ωi. Afterward, she lowers it onto the ground. Just when the cylinder's surface touches the ground, the speed of the center of mass of the cylinder is zero. Though in the beginning, the cylinder skids on the ground eventually it rolls without skidding. Given that the moment of inertia of the solid cylinder about the rod is I = 1/2 mR2, and the coefficient of friction between the cylinder and the ground is μ, determine for how long the cylinder skids on the ground before it rolls without skidding.
[Hint: Apply ∑F = ma, ∑τcm = Icmαcm, and consider that vcm = ωr only when the cylinder rolls without skidding.]
