A solid homogeneous cylinder of radius R starts from rest at the edge of the fixed block and rolls without slipping about the edge. Which option gives the correct complete set: (i) angle θ꜀ at loss of contact, (ii) centre speed just before loss of contact, and (iii) K(translational)/K(rotational) when the centre is horizontally level with the edge?

Question

G1 Physics · Accepted Answer

Use energy while the cylinder rolls about the edge without slipping. With I about CM=½MR², the instantaneous inertia about the edge is I about the edge=I about CM+MR²=3MR²/2. Loss of gravitational potential energy gives ω(θ), and the normal reaction becomes zero when the radial equation is just satisfied. This yields cosθ꜀=4/7, v=√(4gR/7), and K translational/K rotational=6. Hence option A.