Reaction on the particle in terms of angular velocity

[kuruman]

Almost there. You need to solve for N not ω, that is have N by itself on the left side of the equation.

 

[moenste]

Almost there. You need to solve for N not ω, that is have N by itself on the left side of the equation.

Hm, it indeed gets to N = m (g - 0.4 ω²). And that is the reaction on the particle in terms of ω?

 

[kuruman]

Yes it is. IMO it would have been clearer to have asked for the normal force in terms of ω.