An amusing trick is to press a finger down on a marble on a horizontal table top, in such a way that the marble is projected along the table with an initial linear speed v and an initial backward rotational speed ω about a horizontal axis perpendicular to v. The coefficient of sliding friction between marble and top is constant. The marble has radius R. If the marble skids to a stop and then starts returning toward its initial position, with a final constant speed of 0.620v, what was ω in terms of v and R? Hint for part (b): When the marble rolls without slipping, the relationship between speed and angular speed is v = ωR.

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