# What would the moment of inertia of a hollow cylinder a distance to the axis of rotation be? [closed]

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.

• Use the Parallel Axis Theorem Nov 5 '21 at 18:56
• 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? Nov 5 '21 at 19:08

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