The rotational kinetic energy ($K$) is related to angular momentum ($L$) and moment of inertia ($I$) by the relation $K = \frac{L^2}{2I}$. Given that the kinetic energies of rotation are equal: $K_A = K_B$. $\frac{L_A^2}{2I_A} = \frac{L_B^2}{2I_B}$ Rearranging the terms, we get: $\frac{L_B^2}{L_A^2} = \frac{I_B}{I_A}$ It is given that $I_B > I_A$, so the ratio $\frac{I_B}{I_A} > 1$. Therefore, $\frac{L_B^2}{L_A^2} > 1 \implies L_B^2 > L_A^2 \implies L_B > L_A$.