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A coin on a rotating turntable begins to slip when placed 4 cm from the center. If the turntable's angular speed is doubled, at what distance from the center will the coin just start to slip?

1. 1 cm
2. 2 cm
3. 4 cm
4. 8 cm

Correct answer: 1 cm

Solution

For a coin on a rotating turntable, slipping begins when the required centripetal force equals the maximum static friction. Since $F_c = mr\omega^2$, for the same coin and same friction limit, $r\omega^2$ remains constant. If angular speed is doubled, the limiting radius becomes one-fourth.

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