The free end of a string wound on a solid cylinder of mass M and radius r is pulled upward by force F as shown. The floor is sufficiently rough for pure rolling. What is the maximum angular acceleration possible without loss of contact?

Question

G1 Physics · Accepted Answer

For pure rolling, F and friction determine both translation and rotation: F+f=Ma and (F-f)r=Iα with I=½Mr² and a=αr. The normal reaction must remain non-negative; at the limiting case N=0. Solving the limiting equations gives maximum α=2g/(3r). Hence option D.