Two cylindrical hollow drums of radii R and 2R, and of a commom height h, are rotating with angular velocities omega (anti-clockwise) and omega (clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by (3R + delta). They are now brought in contact (delta rarr 0). (a) Show the frictional forces just after contact. (b) Identify forces and torque external to the system just after contact. (c ) What would be the ratio of final angular velocities when friction ceases ?

Two cylindrical hollow drums of radii R and 2R, and of a commom height

1.	Two cylindrical hollow drums of radii R and 2R, and of a commom height h, are rotating with angular velocities omega (anti-clockwise) and omega (clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by (3R + delta). They are now brought in contact (delta rarr 0). (a) Show the frictional forces just after contact. (b) Identify forces and torque external to the system just after contact. (c ) What would be the ratio of final angular velocities when friction ceases ?
Answer» Solution : Considerthesituation shownbelowwe haveshownthe frictional forces . (B)`F'= F=F` whereF and F are external forces throughsupport `IMPLIES F_("net")=0 ("one each cylinder")` Externaltorque `=Fxx3R` (anti- CLOCKWISE ) ( c)LET`omega _(1)` and `omega_(2)`be finalangularvelocitesofsamallerandbigger drumrespectively(anti - clokwise andclockwise Respectivelty) Hence, `Romega_(2)implies(omega_(1))/(omega_(2))=2` Note :-We shouldbe very carefulwhileindicatingdirectionoffrictional forces.