Minimum force required to rotate a lamina

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Homework Help Overview

The discussion revolves around determining the minimum force required to rotate a lamina about different points (A, B, and C). The problem involves concepts from mechanics, particularly focusing on forces, torques, and frictional effects in a rigid body context.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts two approaches to solve the problem, questioning the moment of inertia and the role of friction. Some participants suggest that friction can be treated as acting at the centroid, while others challenge the assumption of uniform friction across the lamina. There are discussions about the implications of angular acceleration and the forces acting on the lamina.

Discussion Status

The discussion is ongoing, with participants exploring various interpretations of the problem. Some have offered tentative justifications for their reasoning, while others are questioning the validity of assumptions made regarding friction and acceleration. There is no explicit consensus yet, but several productive lines of inquiry have been initiated.

Contextual Notes

Participants note constraints such as the requirement to use high school physics principles and the challenge of calculating the moment of inertia for the lamina. There is also mention of the need to consider internal constraint forces in the analysis.

  • #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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