Minimum force required to rotate a lamina

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The discussion centers on determining the minimum force required to rotate a lamina about different points (A, B, and C). Two approaches are explored: the first involves calculating forces and torques but encounters difficulties with the moment of inertia and lengthy calculations. The second approach suggests that the minimum force to rotate the lamina about one point must also be sufficient for rotation about the others, but this leads to incorrect results. The participants debate the assumptions of uniform friction and internal constraint forces, ultimately concluding that friction may not be uniform across the lamina. The conversation highlights the complexities of applying static equilibrium and torque principles in rigid body dynamics.
  • #31
PhysicsBoi1908 said:
how do we conclude that magnitude of friction is constant
The weight per unit area is constant. When the lamina moves, all parts go into kinetic friction, so when it is about to move all parts must be at max static friction.
 
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  • #32
Ah! Thank you very much.
 
  • #33
haruspex said:
I see a way.
Drop a perpendicular from C to meet AB at D. Consider the torques required to rotate the two smaller triangles about C.

It is very clever! If you don't explicitly cut the lamina there will be an internal force between the two parts. The result is that the torque you have to apply at A/B is slightly more than calculated and the torque you have to apply at B/A is slightly less than expected. But these two discrepancies will cancel exactly, and their sum will just be the same as if the lamina were not actually connected, except at the hinge (i.e. no internal force between the two parts).
 

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