V Track

A track consists of two rough planes forming an angle 2θ to each other. It's symmetric to vertical axis and makes an angle φ to the horizontal.
Coefficient of friction of the planes are different. The left side is μ0 and the right side is μ.
Then a ball of radius R and mass M (moment inertia I=ηMR^2) is placed on the track.


As the ball moves, it slips with left side of the track and does not slip with right side of the track.
Find the minimum value of μ! (in μ0, φ, and θ)


Click here to read the solution.