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A coin rests on a gramophone record rotating at angular velocity \(\omega\). The coefficient of static friction is \(\mu\). The coin rotates without slipping if its distance \(r\) from the center satisfies:

1. r = mu*g/omega²
2. r <= mu*g/omega²
3. r >= mu*g/omega²
4. r > mu*g/omega²

Correct answer: r <= mu*g/omega²

Solution

For no slipping, static friction must provide the centripetal force \(m\omega^2 r\). Since the maximum static friction is \(\mu mg\), we need \(m\omega^2 r \le \mu mg\), which gives \(r \le \mu g/\omega^2\).

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