Coin or beaker on a rotating disc: condition on angular velocity or distance for it not to slip

1. A.
   $R \leq \frac{\mu g}{2\omega^{2}}$
2. B.
   $R \leq \frac{\mu g}{\omega^{2}}$
3. C.
   $R \geq \frac{\mu g}{2\omega^{2}}$
4. D.
   $R \geq \frac{\mu g}{\omega^{2}}$

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1. A.
   $\frac{\mu g}{r}$
2. B.
   $\sqrt{\frac{r}{\mu g}}$
3. C.
   $\sqrt{\frac{\mu g}{r}}$
4. D.
   $\frac{\mu}{\sqrt{rg}}$

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