First I want to introduce a exercise I tried to solve, and then the doubt I have at the final resolution. "In a slope with θ angle to the horizontal plane, a homogen ball with radius R and mass m roll down without slipping. Calculate the friction force." Force equilibrium ma = mg sinθ - Ff (Ff is friction force) Second Newton La Ff.R = I.γ (γ is angular acceleration) Ff = (2/5)γmR Condition of non-slipping a=γR Ff = (2/5)ma Ff = mgsinθ-ma = (2/5)ma -> a =(5/7)g sin θ And Ff = (2/7)mgsinθ Ok, now is the doubt. a) Doesn't friction force depends on static friction coefficient of the slope with the ball? b) In case the static friction coefficient was μ, and μ< (2/7)tanθ ( in this case the maximum friction force would be < (2/7)mgsinθ, and we couldn't have the force above), what would happen?