A horizontal uniform circular disk has a mass $2m.$ The disk is free to rotate about the $z$ axis and initially at rest. A man having mass $m$ begins to run along the edge in a circular path whose radius is approximated to be $R.$ If he maintains a speed of $v_0$ relative to the disk, what is the angular velocity of the disk? Neglect friction.

$\frac{v_0}{R}$

$3\frac{v_0}{2R}$

$2\frac{v_0}{3R}$

$\frac{v_0}{3R}$

$\frac{v_0}{2R}$

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