On a rough floor with coefficient of kinetic frction \( \mu_k \), a horizontally placed uniform circular disk of radius \(R\) is rotating about a fixed point on it's circumference with angular velocity \( \omega_0 \).

The time taken by the disk to stop is \(t = \dfrac{a}{b} \dfrac{\pi R \omega_{0}}{\mu_{k} g}\), where \(a\), and \(b\) are positive coprime integers. Find the value of \(a+b\).

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