POSSIBLE SOLUTION(S)

1) How thick is the tape?

2) Derive a function that gives the tape spindle driver speed (in rotations per minute -- rpm) as a function of the radius.

We require the tape speed to remain constant, so the spindle speed will have to vary with the radius of the tape:

Input := 

SpindleSpeed[radius_] := TapeSpeed/(2 Pi radius)
Plot[SpindleSpeed[radius],
 {radius, RadSpind, RadWound},
 AxesLabel -> {"radius of wound tape [in]", "rpm"},
 PlotRange -> {{0, 2}, {0, 1}}]

Output =

-Graphics-