$(3$ pts$)$ A diver in the full layout position is rotating with an angular velocity of $8ra\frac{d}{s}$ and a moment of inertia of $10k{g}^{**}{m}^2.$ When he goes into the tucked position, his moment of inertia is reduced to $3k{g}^{**}{m}^2.$ How long will it take him to rotate through an angle of $540$ in the tucked position?

Time to rotate $540$ :