$μ_s=0.35$ and $μ_k=0.25$ determine the value of P for imending motion up the plane.

$$∑f_y =0$$

$N-mg=0 \\ N=mg$

By Newton’s 2nd law,

$F=ma \\ μ\space N=ma \\ 0.4 ×m ×9.81=m ×a \\ a_n=3.924 m/s^2 \\ a_n= \dfrac {V^2}ρ \\ V=\sqrt{a_n.ρ} = \sqrt{3.924 ×0.5} =1.4m/s$

Angular velocity,

$W = \dfrac Vr = \dfrac {14}{0.5} = 2.8 rad/s \\ W=2.8 rad/sec$