A coin 20mg is place on the smooth edge of a 25 cm-radius phonograph record as the record is brought up to its normal rational speed of 45 rmp. What must be the coefficient of friction between the coin and the record if the coin is not to slip off

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Newton's First Law of Motion

If a very smooth ball is rolled down an inclined surface with zero friction, the ball will continue to roll indefinitely for an infinite time, in an attempt to reach to the same height on the opposite hill!