A spool of thread consists of a smaller cylinder of radius R/2 in the middle and two discs of radius R fixed to its two ends. The thread is wound on the cylinder. The spool of mass m is placed on a horizontal table, then the end of the thread is pulled in a direction shown in the figure. a) What is the angle α between the thread and the vertical if the center of the spool does not move neither to the left nor to the right? (Assume that the spool does not slip.) b) What is the coefficient of static friction between the spool and the table if the spool slips when the pulling force reaches a certain value F0?

A spool of thread consists of a smaller cylinder of radius R/2 in the middle and two discs of radius R fixed to its two ends. The thread is wound on the cylinder. The spool of mass m is placed on a horizontal table, then the end of the thread is pulled in a direction shown in the figure. a) What is the angle α between the thread and the vertical if the center of the spool does not move neither to the left nor to the right? (Assume that the spool does not slip.) b) What is the coefficient of static friction between the spool and the table if the spool slips when the pulling force reaches a certain value F0?