Removable Whorls are usually circular and have a hole in the middle. This hole can match your spindle stick taper perfectly or not.
1. Tapered Whorl Holes are superior when their taper matches the spindle stick taper for perfect fit
This match between inside and outside tapers yields maximum whorl stability - the spindle shaft and whorl hole are touching all the way down the hole. The whorl is harder to slide off the spindle shaft in use. Not perfect, though. It is always helpful to wrap a tiny hair rubber band to the bottom of the whorl to prevent sudden in-spin flight to unknown spots on the floor or, worse, in the grass.
2. Straight-sided whorl holes will touch down on the tapered shaft at their top, leaving the the rest of the hole unsupported all the way to the bottom of the whorl. This makes the bottom of the whorl wiggly; the whorl won't remain balanced 'cause it can move around. You can test this by checking for sideways WIGGLE.
3. Tapered Whorl Holes that DON'T match the spindle shaft taper usually bind on the shaft at the bottom of the whorl.
This leaves the top of the hole loose and free to wiggle. The solution is to wind a tiny hair rubber band (maybe two…) on the spindle shaft above the top of the whorl and push it down into the sloppy hole to stabilize the wiggle. Don't forget to prevent 'in-spin flight' by also adding a tiny rubber band under the whorl too. This saves a lot of time crawling around the floor looking for your whorl. They don't fall in a straight line, but act like little curve balls.
4. Thin Disc-Shaped Whorls introduce wobble due to the lack of sufficient surface area on the inner hole walls. There isn't enough to grip the spindle shaft firmly. Sometimes placing rubber bands above and below the whorl can stabilize this type of whorl enough to stay balanced.
5. Flat out Unbalanced Whorls. The very first thing to try when a whorl is causing your spindle to 'judder' is to rotate the whorl on the stick about 1/4 turn. Continue to study the effect of this when the spindle is rotated. Sometimes the spindle is also unbalanced. By rotating the whorl, you might find the sweet spot that gives good balance or help to seat the whorl in a better place on the spindle. If this fails to remove the judder, you might have an unbalanced whorl. This will decrease the spin time of your flick. What is amusing to the modern reenactor is a LOT of Viking and Medieval spindle whorls were unbalanced. They used them anyway, what can I say. Guess they simply had a get-er-done attitude about making yarn before the winter came.
6. Riding High and Riding Low. Removable whorls are dependent on spindle shaft taper in terms of where they will be fixed. Some will tuck high under the 'belly' of a spindle. Some ride quite low towards the bottom. Some length of spindle needs to be left below a low-riding whorl. That extra spindle length adds stability to the spin.
When testing whorl locations out, you'll find there is a difference in riding high and low. Experiment!
7. Badly finished found objects used as whorls. There are large beads out in commerce land that have been torn from molds. Their holes are ragged. Their balance is not even. You CAN use them. But the damage they do to a shaft is significant every time it is jammed on. That holds true for other metal materials as well.