Two cylindrical hollow drums of radii R and 2R, and of a common 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 $(3\text{R}+\delta).$ They are now brought in contact $(\delta\rightarrow0){:}$
- Show the frictional forces just after contact.
- Identify forces and torques external to the system just after contact.
- What would be the ratio of final angular velocities when friction ceases?
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- The frictional forces acting between two cylindrical hollow drums are as shown in the diagram below:
Force F downward shows the friction force on right drum.
- $F^1 = F = F”$ where $F^1$ and $F”$ are external forces through support.
Net external torque to the system about any axis = $Fx_3R$, anticlockwise,
- Let $R_1$ and $R_2$ be final angular velocities of smaller and bigger drum respectively (anticlockwise and clockwise respectively).
$^vA = ^vB$
Hence, $R_1 = 2R_2$
Important point: Friction force just opposes the relative motion of point of contacts at any instant. So, we should be very careful while indicating direction of frictional forces.
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