This is a part in the solution of the first exercise in Princeton problems in ph

Question

This is a part in the solution of the first exercise in Princeton problems in physics with solutions.
When I proved final angular speed had to be equal to initial angular speed from conservation of energy I obtained the expression of the rotational kinetic energy (1/2I^2) instead of I^2 (what is printed).
Am I wrong or it is a typo?
Thanks

We may also derive the condition w from conservation of energy. For completeness, this derivation follows. Because the collision is elastic, energy is conserved. The magnitude of the momentum in the y-direction is unchanged by the collision, so the energy balance equation becomes (10.5) vl, it mu can see that vi =-v, requires ui--wf.

Explanation / Answer

I don't know the complete problem but definitely there should be 1/2 there in the expression for rotational kinetic energy.

Rotational kinetic energy= 1/2 I w2

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