# A very Edgy Problem!

**Classical Mechanics**Level 5

**I**: \(\theta_c\) is the angle through which the cylinder rotates before leaving the plane of the table

**II**: \(v_{cm} \) is the speed of the centre of mass of the cylinder just before leaving the plane of the table

**III**: \(c\) is the ratio of the translation to rotational kinetic energies of the cylinder when its centre of mass is in the horizontal line of the edge.

Evaluate \( \Large 7\cos\!\theta_c + v_{cm} + c\).

**Details and Assumptions**

Sufficient friction is present so that even a very small displacement causes rotation without slipping.

Radius of the cylinder \(R = 0.7\text{ m} \).

Take \(g = 10\text{ ms}^{-2} \).