Yeah but this can get mad expensive for something not worth the cost, unless you write a dispatch API to 5000 free cloud accounts to make use of their 5000 free cloud credits.

D3 is definitely the way to go (also will probably give better performance than the cloud), but it's a non-trivial export process.

Is there more code than what you posted? It seems to be incomplete when I try and run the notebook - missing functions for theta[t]. It also seems that you could publish something similar to what you can find on the Wolfram Demonstrations Projects website and it would work just fine for this use-case. Hell - I might even put it right on the Demo Website itself.

You can try exporting as cdf, but you had better making the panels self-contained, without relying on separate sliders:

g = 9.81;
rdot = 0.05;
theta0 = 0.2;
thetadot0 = 0;
s = ParametricNDSolveValue[{theta''[t] == 
     Sin[theta[t]]*Cos[theta[t]]*omega^2 - g/r0*Sin[theta[t]], 
    theta[0] == theta0, theta'[0] == thetadot0}, 
   theta, {t, 0, 100}, {omega, r0}];
Manipulate[
 Graphics[{Blue, Circle[{0.0, 0.0}, r0], Black, 
   Line[{{-1.2, 0}, {1.2, 0}}], Line[{{0, -1.2}, {0, 1.2}}], Black, 
   Inset[Style[NumberForm[t, {3, 2}], 20], {1.0, 1.1}], Red, 
   Disk[{r0*Sin[s[omega, r0][t]], -r0*Cos[s[omega, r0][t]]}, rdot]}],
 {t, 0, 100, 0.001, Animator, AnimationRunning -> False, 
  AnimationRepetitions -> 1, AnimationRate -> anrate},
 {anrate, 0.1, 1, 0.05},
 {omega, 0, 20, 0.5},
 {{r0, 1}, 0.01, 2, 0.1}, SaveDefinitions -> True]