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Almost there. You need to solve for N not ω, that is have N by itself on the left side of the equation.
Reaction on the particle in terms of angular velocity
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The discussion revolves around calculating the reaction force on a particle moving in a circular motion on a table, connected by a string. The key equations derived include the relationship between the reaction force (N), gravitational force (mg), and angular velocity (ω), leading to the expression N = m(g - 0.4ω²). Participants clarify that the reaction force approaches zero when the particle is on the verge of lifting off the table, indicating the maximum angular velocity condition. The maximum angular velocity is also confirmed to be ω = √(5g/2). The conversation emphasizes the importance of distinguishing between tension and normal force in the context of the problem.
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