I read an article now and it confused me completely. Since I thought I have read somewhere else a completely different solution.
You put a ball on an incline at rest. What is the minimal friction force so that the ball rolls without slipping?
I thought there is a simple and easy solution. All you need is that the sigma forces in X axis would be equal at least to zero. Which is the minimum, or else the friction could be stronger.
But I have read this article https://www.google.co.il/url?sa=t&source=web&rct=j&url=http://www.feynmanlectures.info/solutions/roll_without_slipping_sol_1.pdf&ved=0ahUKEwig-tinj4DbAhWCBZoKHextDoEQFghtMBQ&usg=AOvVaw1T-CXiuqp0CtO1W2NNFzbY and he has long calculations for it.
I don't really understand why????
I am trying to think about it and my solution seems perfectly correct. There isn't any force that rotates the ball apart from friction. So the ball will certainly rotate as long as it doesn't slip. And it doesn't slip when the friction is equal or stronger than the X component of the MG force of gravity.
Isn't it sufficient to say that MGsin(a)= F friction?
Isn't it enough? Why are there so much complexity in the article? And why is it correct?