From Mechanics

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Current revision

Converting the angular speed to standard units.

\displaystyle \omega =30\text{ rpm }=\frac{30\times 2\pi }{60}=\pi \text{ rad}{{\text{s}}^{\text{-1}}}

For circular motion:

\displaystyle \begin{align} & F=mr{{\omega }^{2}} \\ & =0\textrm{.}02\times 0\textrm{.}25\times {{\pi }^{2}} \\ & =0\textrm{.}0493\text{ N} \end{align}

The force \displaystyle R on the coin normal to the surface is

\displaystyle R=9\textrm{.}8\times 0\textrm{.}02=0\textrm{.}196\text{ N}

Using the friction inequality for the coin to remain at rest on the surface:

\displaystyle \begin{align} & F\le \mu R \\ & F\le 0\textrm{.}6\times 0\textrm{.}196 \\ & F\le 0\textrm{.}1176\text{ N} \\ \end{align}

As 0.0493 is less than 0.1176 the coin remains in the same position on the turntable.