How do you solve this?
Mechanics Exercise
F
A roll of thread lies on a table. The spool of thread consists of three cylindrical parts, each of which has a mass of m = 20 grams, see the picture showing the spool of thread from two sides. The two outer cylinders have radius R = 3 cm.The thread is wound up in a thin layer on the middle cylinder, which has a radius of R/2. The central hole in the parts can be neglected, and the mass distribution in each part is homogeneous. A student studies the movement of the spool of thread by pulling on the thread with the force F
as shown in the figure.The amount of the force is 0.25 N and the angle = 25o.The student tests the thread roll's movement on different surfaces,with different coefficients of friction. You can assume that the student pulls very carefully so that the movement is planar movement, i.e. that the roller moves in a straight line and does not bend. Amount and direction of accelerations and angular accelerations must be clearly stated in the answers. The direction can e.g. specified as right/left or clockwise/counterclockwise, or in a specified coordinate system.
(a) Determine the smallest possible value of the coefficient of friction us for the roller to roll without slipping.
(b) Determine the acceleration of the spool of thread and its angular acceleration if us = 0.1.
(c) Determine the acceleration of the spool of thread and its angular acceleration if s = 0.6.