Final answer:
When a skater pulls in her arms, her rotational inertia decreases and her spin rate increases due to the conservation of angular momentum, not because of an increase in rotational inertia, making the statement false.
Step-by-step explanation:
When an ice skater spins with her arms outstretched and then pulls in her arms close to her body, several principles of physics come into play. The statement that is false among the given options is b) Increase in rotational inertia. When the skater pulls her arms in, she decreases her moment of inertia, which means her rotational inertia decreases, not increases. Conservation of angular momentum dictates that her angular velocity must increase to keep the angular momentum constant since the net torque is negligibly small. During this process, the total mechanical energy is conserved, which means no kinetic or potential energy is lost to the environment. Therefore, conservation of energy still holds true in this scenario.