From Mechanics

If \displaystyle F=\mu R then the coin can remain on the surface. This is the maximum value that \displaystyle F can take.

That is \displaystyle mr{{\omega }^{2}}=\mu R.

This gives

\displaystyle \begin{align} & 0\textrm{.}02\times r\times {{\pi }^{2}}=0\textrm{.}1176 \\ & r=\frac{0\textrm{.}1176}{0\textrm{.}02\times {{\pi }^{2}}}=0\textrm{.}596\text{ m or 59}\text{.6 cm} \\ \end{align}

Note that for values of \displaystyle r greater than this the frictional force cannot keep the coin from sliding.