Axis along cylinder height
I = I_cm + md²
Where I_cm is the moment of inertia about the center of mass, m is the mass, and d is the perpendicular distance between axes.
Moment of inertia, also known as rotational inertia or angular mass, is a quantity that determines the amount of torque needed for a desired angular acceleration about a rotational axis. It is the rotational analog of mass in linear motion. Just as mass resists linear acceleration, moment of inertia resists angular acceleration.
The moment of inertia depends not only on the mass of an object but also on how that mass is distributed relative to the axis of rotation. Objects with more mass concentrated farther from the axis have larger moments of inertia. This is why figure skaters spin faster when they pull their arms in - they're reducing their moment of inertia.
Moment of inertia calculations are based on idealized formulas assuming uniform density and perfect geometric shapes. Actual values may vary due to non-uniform mass distribution, shape imperfections, and axis placement. Consult engineering references and perform physical testing for precise analysis in critical applications.