Final answer:
If another Earth-sized planet were added to our solar system, the moment of inertia of the system would increase, and the angular velocity would decrease as a result, assuming the system is isolated and conserves angular momentum.
Step-by-step explanation:
If another planet the same size as Earth were put into orbit around the Sun along with Earth, the moment of inertia of the solar system would increase. This is because the moment of inertia is a measure of how much torque is needed for a certain angular acceleration about an axis, which depends on the distribution of the mass relative to the axis. Adding another Earth-sized planet adds to the mass distribution of the system.
The angular velocity of such a system, if isolated, would decrease as a result of the increased moment of inertia, according to the conservation of angular momentum.
For example, when a child on a rotating merry-go-round moves closer to the center, the system's moment of inertia decreases, causing the angular velocity to increase to conserve angular momentum. This analogous situation helps to understand how changing the distribution of mass affects rotational motion.