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So I understand that the inertia of a hollow cylinder about a tangent axis to its surface is $\frac{M}{2}(R_1^2 + 3R_2^2)$, but what if this axis is not a tangent to the cylinder? So it is some distance form the cylinder.

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    $\begingroup$ Use the Parallel Axis Theorem $\endgroup$ Nov 5 '21 at 18:56
  • $\begingroup$ Hey many thanks for your guidance! Therefore, would it be the moment of inertia about the axis passing through the center of mass, plus MR2^2 where R2 is the distance of the axis passing through the center of mass and the axis a distance x from the surface of the cylinder? $\endgroup$
    – Nur Ahmed
    Nov 5 '21 at 19:08
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Using the parallel axis theorem you have

$$\begin{array}{r|l} \text{mass of cylinder} & m \\ \text{radius of cylinder} & R \\ \text{MMOI about center axis} & I_{\rm center} = \frac{m}{2} R^2 \\ \text{rotation axis to center distance} & (x+R)\\ \text{MMOI about rotation axis} & I_{\rm rotation} = \frac{m}{2} R^2 + m (x+R)^2 \\ \end{array}$$

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  • $\begingroup$ Thank you so so much!! I greatly appreciate it!! :D $\endgroup$
    – Nur Ahmed
    Nov 5 '21 at 19:30

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