I expand the comment above: here is a rough example:
I created a "tape" black circle which will be animated (rotated and scaled). Then I put another object just over it, to represent the cassette gear, which has a copy rotation constraint to the tape.
here it is:
Then I animated it over 60 frames, putting 4 "rotscale" keyframes.
Here you see them, and you see the "tape" at frame 1
if you press ALT+A the tape and gear rotate, and "tape disk" becomes smaller...
..and after 60 frames, at 4th keyframe, you get:
Of course you could get much more realistic results, but this is just a fast example to get an inspiration...
here is the .blend I intended to append before
in which, as a bonus, I added a "complete" (simplified) cassette setup:
I used two empties to move the "tape" mesh ends, following the scaled tape gears... see the .blend for more details.