A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radus R is placed horizontally at rest its length parallel to the edge such that the exis of the cylinder and the endg of the block are in the same vertical plane as shown in the figure below. Ther is sufficinet friction present at the edge s that a very small displacement causes the cylinder to roll off the edge without slipping. Determine:

(a) the angle `theta_c` through which the cylinder rotates before it leaves contact with the edge,
(b) the speed of the centre of mass of the cylinder before leaving contact with the edge, and
(c) the ratio of the translational to rotational kinetic energy of the cylinder when its centre of mass is in horizontal line with the edge.

Answer

[`cos^(-1)"(3g)/(2omega^(2)l),1//2momega^(2)lsqrt1+(7g^(2))/(4omega^(4)l^(2)),cosphi=(4costheta)/(sqrt(9+7cos^(2)theta))`]