Accelerationg of rotating mass *along* the axis of rotation

Says Wikipedia: "The moment of inertia is a measure of an object's resistance to any change in its state of rotation".

Now consider a rotating mass [itex]m[/itex] that I would like to accelerate along its axis of rotation by [itex]a[/itex]. Does this count as a "change in its state of motion"? Will it resist the acceleration more that just [itex]F=m\times a[/itex]. And if yes, how much?

Thanks,
Harald.