Minimum force required to rotate a lamina

Click For Summary
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.
 
  • Like
Likes PhysicsBoi1908
Physics news on Phys.org
  • #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).
 

Similar threads

To find the centre of gravity of a lamina
  • · Replies 2 ·
Replies
2
Views
2K
To find the resultant of forces on a lamina
  • · Replies 5 ·
Replies
5
Views
3K
How Do You Calculate the Moment of Inertia for Combined Square Laminas?
  • · Replies 3 ·
Replies
3
Views
3K
To find the tipping point of a lamina
  • · Replies 2 ·
Replies
2
Views
1K
Calculating acceleration of gravity and inertia of irregular lamina
  • · Replies 10 ·
Replies
10
Views
5K
Tetrahedron with 3 points fixed, and force applied to 4th
  • · Replies 11 ·
Replies
11
Views
2K
Moment of Inertia perpendicular to lamina
  • · Replies 1 ·
Replies
1
Views
2K
Euler's Equations, a freely rotating lamina
  • · Replies 2 ·
Replies
2
Views
6K
I Resolve moment of inertia at an angle
  • · Replies 2 ·
Replies
2
Views
2K
Moment of inertia of a square lamina through a diagonal
  • · Replies 9 ·
Replies
9
Views
23K