If you want the reel to spin about the central axle hole, you're going to need to model this in 3D. The object is simple enough that you could do it with extruded shape layers and the ray-traced 3D renderer, but I'd probably do this in Cinema 4D, since you can use Cinema 4D .c4d scene files in After Effects (and Cinema 4D Lite is included with After Effects).
If you want to do this entirely inside AE your graphic is wrong. You need to build up the object with straight on views each a separate layer and then stack them up inside AE as 3D layers. You offset each layer in Z by one pixel using an expression like this: [value, value, index]
Then you parent all of the layers to a 3D null and animate the rotation property. Adding a light helps the effect. Your project would look like this if you made it all with shape layers:
You could also use RayTraced rendering and extrude the reel parts. The theory is the same. You build up your object using flat layers then parent them to a 3D null to group them, then add lights and cameras. You just can't do it with artwork that is already in perspective.
Here's a CC project file tor you to dissect. FilmReelFromShapeLayers_CC.aep (Note: DropBox is probably going to add a .txt extension after the .aep. Just delete it so the name of the file is FilmReelFromShapeLayers_CC.aep)
There's also a Ray-Traced version for you to play with if your system has a compatible NVIDIA card or you want to struggle with incredibly long render times.
Thanks Rick for the sample project and both of you for the suggestions. I'll read more on Ray Traced and Cinema 4D.
Looks like a good learning project.