Around which points to make T=I(alpha)

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Homework Help Overview

The discussion revolves around the application of the rigid body angular momentum formula T=Iα in the context of a cylinder rotating on a rough surface with a steady force acting on its center. Participants explore the implications of calculating angular acceleration around different points, specifically the center of mass and points on the cylinder, questioning the consistency of results obtained from these calculations.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the validity of using the formula T=Iα around various points, noting discrepancies in results when calculated around different points. There are inquiries about the role of friction and the conditions under which the formula holds true. Some participants question the assumptions made regarding the motion and forces acting on the cylinder.

Discussion Status

The discussion is active, with participants providing insights and alternative perspectives on the calculations. Some guidance has been offered regarding the application of the parallel axis theorem and the conditions under which angular momentum is conserved. However, there is no explicit consensus on the interpretations being explored.

Contextual Notes

Participants are navigating the complexities of angular momentum and torque calculations, with some expressing uncertainty about the derivation of certain equations and the implications of their assumptions. There are references to missing information and the need for clarity on the role of friction in the problem setup.

  • #31
I want to find (alpha), but I don't succeed:

\left(F\frac{R}{2}+f \frac{R}{2}\right)\hat{z}=KmR^2\vec{\alpha}+\left(\frac{R}{2}\cdot\frac{RF}{m(K+1)}\right)\hat{z}

\frac{FR(2K+1)}{2(K+1)}=KmR^2\cdot \alpha+\frac{FR^2}{2m(K+1)}

Which doesn't give the previous (alpha).
 

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