In the figure, a $5\mathrm{.}50g$ bullet is fired into a $0\mathrm{.}380kg$ block attached to the end of a $0\mathrm{.}778m$ nonuniform rod of mass $0\mathrm{.}159kg.$ The blockrod$-$bullet system then rotates in the plane of the figure, about a fixed axis at $A.$ The rotational inertia of the rod alone about $A$ is $0\mathrm{.}0590kg*m^2.$ Treat the block as a particle. $($a$)$ What then is the rotational inertia of the block$-$rod$-$bullet system about point $A?($b$)$ If the angular speed of the system about A just after impact is $8\mathrm{.}87ra\frac{d}{s},$ what is the bullet's speed just before impact?

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