According to the law of conservation of angular momentum, if no external torque acts on a system, its angular momentum ($L$) remains conserved (constant). When the radius ($R$) of the sphere is increased while keeping its mass ($m$) constant, its moment of inertia ($I \propto mR^2$) increases. Since $L = I\omega$ is constant, the angular velocity ($\omega$) must decrease to compensate for the increased moment of inertia. Furthermore, the rotational kinetic energy is given by $K = \frac{L^2}{2I}$; since $L$ is constant and $I$ increases, the rotational kinetic energy will also decrease. Therefore, only the angular momentum remains unaffected.