The system is released from rest with the cable taut, and the homogeneous cylinder does not slip on the rough incline. determine the angular acceleration of the cylinder and the minimum coeffi cient s of friction for which the cylinder will not slip.

hello your question is incomplete below is the complete question

answer : Angular acceleration = 7.88 rad/s^2 ( clockwise )

              minimum coefficient of friction = -0.2225

Explanation:

First step : we calculate acceleration at point O

a = rα

acceleration at point A

aA = ( 2r ) α  = 2α

∑Fy ( force in y axis ) = mass of block * aA

∴ T = mBlock ( g - 2α )

      = 8.7 ( 9.81 - 2α )

attached below is the remaining part of the solution

work: w = fd (given)

work done by chet   =50*1 = 50 j

work done by mika =40*2 = 80 j

work done by sara =30*1.5 = 45 j

work done by bill =60*0.5 = 30 j

students in order from the greatest amount of work done to the least is mika> chet> sara> bill

hence option (b) is correct.

massxgravity x heght=weightxheight= pe

4900=490xh

h=10