Around which points to make T=I(alpha)

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The discussion centers on the application of the angular momentum formula T=Iα around different points for a cylinder rotating on a rough surface. Calculations show consistent angular acceleration (α) results when using points A and C, but a different result arises when using point B, indicating the importance of the chosen reference point. The conversation highlights the necessity of including friction in calculations and clarifies that the parallel axis theorem is applicable primarily at the center of rotation. Participants also delve into the derivation of angular momentum equations and the significance of the center of mass in these calculations. The thread concludes with a focus on the complexities of deriving angular acceleration and the nuances of applying these principles correctly.
  • #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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