A marble of inertia \(m\) is held against the side of a hemispherical bowl as shown in Figure P12.69 and then released. It rolls without slipping. The initial position of the marble is such that an imaginary line drawn from it to the center of curvature of the bowl makes an angle of \(30^{\circ}\) with the vertical. The marble radius is \(R_{\mathrm{m}}=10 \mathrm{~mm}\), and the radius of the bowl is \(R_{\mathrm{b}}=100 \mathrm{~mm}\). Determine the rotational speed of the marble about its center of mass when it reaches the bottom.

Data from Figure P12.69

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center of curvature 130