1. The problem statement, all variables and given/known data A ball is rolling down from the top of a rough spherical dome with negligible initial velocity and angular velocity. Show that the ball must slide before losing the contact with the dome. 2. Relevant equations ΣF=ma Στ = Fr = Iα fs = μsN vcm = rω Δmgh = 0.5mvcm2 + 0.5Icmω2 I = 2(mr2)/5 3. The attempt at a solution Along the sphere: ΣF = ma mgsinθ - fs = matan Along radius of the sphere: mgcosθ - N = marad Στ = Fr = Iα fsr = Iα Let θ1 be where the ball lose contact. R be the radius of the sphere, r be the radius of the ball. mgh = 0.5mvcm2 + 0.5Icmω2 mg(R+r)(1-cosθ1) = 0.7mvcm2 When N=0, mgcosθ1 = marad gcosθ1 = vcm2/(R+r) vcm2 = (R+r)gcosθ1 mg(R+r)(1-cosθ1) = 0.7(R+r)mgcosθ1 cosθ1 = 1/1.7 θ1 = 54.0° Let θ2 be where the ball starts to slide. To show that the ball slides before it lose contact, θ2 < θ1 When is starts to slide, fs = μsN fsr = Iα μsN = 2mrα/5 N = 2mrα/5μs And if I sub it in to the equations, it gets pretty complicated. I can't solve for θ. So how do I continue from here?