As shown in figure, the forces acting on the block are the gravitational force mg, the normal reaction N, the static friction f, and the cenrifugal 
force with f = μ_sN, P = mω²r. Thus the conditions for equilibrium are 
mg sin θ = P cos θ + μ_sN,
N = mg cos θ + P sin θ
Hence mg sin θ = P cos θ + μ_s mg cos θ + μ_s P sin θ,
giving P $\left(\frac{\mathrm{sin\theta }-{\mathrm{\mu }}_{\mathrm{s}}\mathrm{cos\theta }}{\mathrm{cos\theta }+{\mathrm{\mu }}_{\mathrm{s}}\mathrm{sin\theta }}\right)$=  mg = mω²r,
or ω² = $\left(\frac{\mathrm{sin\theta }-{\mathrm{\mu }}_{\mathrm{s}}\mathrm{cos\theta }}{\mathrm{cos\theta }+{\mathrm{\mu }}_{\mathrm{s}}\mathrm{sin\theta }}\right)$ = $\frac{\mathrm{g}}{\mathrm{r}}$ =  $\left(\frac{\frac{3}{5}-\frac{1}{4}\mathrm{·}\frac{4}{5}}{\frac{4}{5}+\frac{1}{4}\mathrm{·}\frac{3}{5}}\right)$ $\frac{9.8}{4}$= 1.03
ω = 1.01 rad/s