Time for falling down the incline (Rotating Solid Cylinder)

[haruspex]

there is a mistake in your equation.

ehild

That's an alpha (α), not an a.

 

[haruspex]

Are you suggesting that we should assume this constraint and from this we find the static frictional force F and then prove that this F < μ_sN . Thereby concluding that since the frictional force required for rolling without slipping is less than μ_sN , rolling without slipping occurs .

But if we had obtained F > μ_sN , we could have argued that slipping does occur as friction is not sufficient .

Am I understanding it correctly ?

Yes.