# Colliding cylinders

**Classical Mechanics**Level 5

A solid cylinder of radius *R* is rolling without slipping on a rough horizontal surface. It collides with another identical cylinder which is initially at rest on the surface. The coefficient of restitution for the collision is 1.The coefficient of friction between the cylinders and between each cylinder and the ground is \(\mu\).If the final angular velocity of the second cylinder after it starts pure rolling is \( \dfrac{a}{b}\) where *a* and *b* are coprime positive integers find *a*+*b*.

**Given**

\(\bullet\)Initial velocity of centre of mass of the first cylinder is 17.5 m/s,

\(\bullet\)\(R=1m\)

\(\bullet\)\(\mu \)=0.5