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प्रश्न
Two cylindrical hollow drums of radii R and 2R, and of a common height h, are rotating with angular velocities ω(anti-clockwise) and ω(clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by (3R + δ). They are now brought in contact (δ → 0).
- 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?
उत्तर
a. The frictional forces acting between two cylindrical hollow drums are shown in the diagram below.
Force F upward shows the friction force on the left drum.
Force F downward shows the friction force on the right drum.
b. F' = F = F” where F and F” are external forces through support.
⇒ Fnet = 0 ......(one each cylinder)
Net external torque to the system about any axis = F × 3R, anticlockwise
c. Let ω1 and ω2 be the final angular velocities of smaller and bigger drums respectively (anticlockwise and clockwise respectively).
Finally, there will be no friction. When friction ceases at the point of contact, then both drums have an equal linear velocity at that point.
VA = VB
Hence, Rω1 = 2Rω2 ⇒ `ω_1/ω_2` = 2
Important point: Friction force just opposes the relative motion of the point of contact at any instant. So, we should be very careful while indicating the direction of frictional forces.
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