Maximizing KE in flywheel energy storage system (KERPS)

1. The problem statement, all variables and given/known data

Describe and explain some of the design features of a flywheel in order for it to store
maximum energy. Your answer should include consideration of the flywheel’s shape,
the material from which it is made and its design for high angular speeds.

2. Relevant equations

KE=Iω2/2
T=Iα
Angular momentum=Iω
I=∑mr2

3. The attempt at a solution

The only part I do not understand about the question is that the answer states that high density material is preferred to increase the mass of the flywheel.

What I am thinking is that, to maximize the kinetic energy of the flywheel, mass of the flywheel must be low because of the conservation of angular momentum.

Since kinetic energy is Iω2/2, an increase in ω results in a greater increase in kinetic energy. Also, since angular momentum is conserved, I must be low for ω to be big.

Since I=∑mr2, mass must be low for I to be low.

What did I get wrong?

Any help would be appreciated.

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