Explain the design considerations for a flywheel rotor, including material selection, shape, and balancing techniques. Discuss the factors that affect the maximum achievable energy storage capacity.

Designing a flywheel rotor for energy storage involves optimizing various parameters to ensure high energy capacity, mechanical integrity, and operational safety. The performance of a flywheel system depends heavily on the rotor’s design, specifically in terms of material selection, shape, and balancing techniques, all of which influence the maximum energy that can be stored and safely utilized.

Material selection is a primary consideration in flywheel rotor design. The energy stored in a flywheel is proportional to its mass moment of inertia and the square of its angular ___ _______ _______ __________ __________ _____ __________ _______ _____ _____.
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