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A small coin is placed on a stationary horizontal disc at a distance \( r \) from its centre. The disc starts rotating about a fixed vertical axis through its centrre with a constant angular acceleration \( \alpha \). Determine the number of revolutions \( N \), accomplishes by the disc before the coin starts slipping on the disc. The coefficients of static friction between the coin and the disc is \( \mu_{g^{\prime}} \)
Figure \( 3.75 \)
(A) \( \frac{\left\{\left(\frac{\mu_{r} g}{r}\right)^{2}+\alpha^{2}\right\}^{1 / 2}}{4 \pi \alpha} \)
B) \( \frac{\left\{\left(\frac{\mu_{s} g}{r}\right)^{2}-\alpha^{2}\right\}^{1 / 2}}{4 \pi \alpha} \)
C) \( \frac{\left\{\left(\frac{\mu_{r} g}{r}\right)^{2}-\alpha^{2}\right\}^{1 / 2}}{2 \pi \alpha} \)
(D) \( \frac{\left\{\left(\frac{\mu, g}{r}\right)^{2}+\alpha^{2}\right\}^{1 / 2}}{2 \pi \alpha} \)
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