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This is my first post on the webpage I hope you guys can help me out. I'm trying to understand the concept of the change of mass moment of inerita through a gearbox. I know the formula, but why does the gear ratio affect the mass moment of inertia [kg m^2]. Let's say you have a input shaft rotating at 540 rpm, a gearbox with a 2:1 ratio, and a disk on the output shaft so why is the inertia "seen" at the beginning of the input shaft equal to the inertia produced by the disk multiplied by 4 considering (effective inertia = inertia x gear ratio^2 ) ?

Maybe you could describe the physics behind this... I sure would appreciate it. Thanks!