1. The problem statement, all variables and given/known data A particle is attached by means of a light inextensible string to a point 0.4 m above a smooth horizontal table. The particle moves on the table in a circle of radius 0.3 m with angular velocity ω. Find the reaction on the particle in terms of ω. Hence find the maximum angular velocity for which the particle can remain on the table Answers: m (g - 0.4 ω2), √5g/2 2. The attempt at a solution At first we find the hypotenuse: 0.42 + 0.32 = 0.52 m. Then we find sin α = 0.6 and cos α = 0.8. The maximum angular velocity is: R cos α = mg (vertical) R sin α = mω2r (horizontal) R = mg / 0.8 and R = mω2r / 0.6 mg / 0.8 = mω2r / 0.6 0.6 mg = 0.8 mω2r g = 0.4 ω2 ω = √5g/2 or 5 rad s-1 (if g = 10). Though I don't know where to start with "Find the reaction on the particle in terms of ω." Isn't it R sin α = mω2r → R = 0.5 mω2? Update: We have R = 0.5 mω2 and R = mg / 0.8 0.5 mω2 = mg / 0.8 0.4 mω2 = mg 0 = mg - 0.4 mω2 0 = m (g - 0.4 ω2) It does fit the answer, but I don't quite understand how zero (0) represents "the reaction on the particle". Any ideas please?