Why do dental drills need such high rpm? Dental drills have always been cutting edge technology when it comes to high rotational speeds. According to Wikipedia modern drills reach more than 180 000 rotations per minute (rpm), which is 3000 rotations per second! For comparison, household drills operate at around 1000 rpm. Obviously a dental drill operates much smoother than a concrete drill, but what's less obvious to me is why?
I could imagine that conservation of angular momentum make the rotational movement less sensitive to external forces. On the other hand a small misplacement of the center of mass with respect to the axis of rotation would cause severe juddering.
Another big difference is that the surface of the dental drill is much smoother than that of a concrete drill. Clearly, with a smoother surface there are many small impacts on the surface per second, while a rough surface leads to less, but more intense impacts. But a smooth drill being operated with low rpm would give rise to few small impacts, isn't that even smoother? The counter-argument to this could be that to drill a hole of a certain size you need a fixed number of impacts and the patients prefer a short treatment.
What are the physical and technical arguments that high rotational speeds have unanimously prevailed in all dentist's offices?
 A: I got this answer from a friend who is an orthodontic surgeon.

Without consulting Wiki (incomplete article) - I can say this off the
top of my head - The rpm is closer to 400 K.
The speed is needed to give the bit/burr some rotational momentum to
provide torque. There is no direct connection between the source of
the energy- compressed air - and the burr. The compressed air is only
at about 2.7 bar and spins a turbine in the head of the drill, which
the burr is attached to. You can hold the burr with your fingers
stationary from start-up - no torque like a concrete bit. Another
mistake in the question is that unlike a concrete drill - most of the
cutting takes place on the side of the burr from a sweeping motion,
not at the tip pushing down on the rotational axis.
What I described here is the high-speed air rotor. The one that makes
the high pitched whine. It has water cooling and lighting (optic
fibers or piezoelectric) built into the head. It is used mostly to
remove enamel with minimum discomfort.  The "slow"  handpiece - up to
200 K rpm has a motor with direct drive through gears to the burr.
Can also have water and fiber optics. Much more torque and vibration.
Does not cut enamel efficiently.  The motor can be driven by compressed
air or electric- more control and torque- more expensive.  The
handpiece can be "regular " to remove caries mostly.  This is known as
a Contra angle handpiece.  More sophisticated ones are required
to place implants and do endo/root canal treatment.  On the same
drive system you also fit a straight handpiece used to cut bone in
surgery. Then you can also cut bone with a piezoelectric handpiece or
a laser.
The one type (air rotor) that I assume the question was about - is
described as an "abrasive device" - not a "drill" as I pointed out.
They also come in the regular head (more torque) and small to reach
inaccessible areas (less torque).
Air Turbine Handpiece
An air turbine handpiece is highly valued as a dental abrasive device
that rotates at a high speed, and it is an essential device for dental
treatment. Since its development, many studies have been conducted to
measure and evaluate rotation performance and measure and evaluate
noise. An air turbine handpiece uses compressed air as the driving
force and is characterized by its small size, lightweight, and
painless abrading at a high rotation speed. However, compared to an
electric handpiece that uses a motor as the driving force, its torque
is small and the noise level is high.
As such, improved performance and reduced noise for an air turbine,
handpiece are desired. Considering that an air turbine handpiece has
the equivalent rotation performance as turbine performance, it can be
considered as a type of turbomachinery, and the fluid mechanics
approach would be effective. In other words, it would be effective to
first elucidate the internal flow of an air turbine handpiece and the
relation between the performance and the noise characteristics and
then control the flow. However, the main component of an air turbine
handpiece, the rotor, is small and rotates at high speeds
(250,000–400,000 min−1); thus, measuring the flow is not easy.
The whole subject is obviously a lot more complicated than the
question posed by the OP.  I think my off-the-cuff answer is adequate
without going into too much technical detail.

Overview
A: Dental enamel is a hard material so the drill needs to exert a large force on it in order to break it. The force is proportional to both the drill radius (r) and it angular frequency ($\omega$, rpm), simply because the speed of the drill material at the interface is $v=\omega r$. So you could go for large $r$ and moderate $\omega$ as for concrete. However dental repair requires narrow holes. This drives the requirement of high angular speed $\omega$.
A: Teeth are brittle, which I painfully know since a school "mate" broke my incisor off during a fight (sudden floor contact). Hence, trying to grind big chunks out of it might cause more damage than intended (e.g. invisible cracks that cause caries years later). It is because bigger chunks require higher forces, no more complicated than that. Consequently one prefers smaller chunks and smaller forces, which requires finer tools and, of course, higher RPM in order to get the same cutting performance.
It is much like grinding tiles. Eagerly using the hammer drill in an attempt to get home from work early might cause the opposite: a huge pile of smashed tiles and no beer'o'clock. Using an angle grinder with high RPM and a diamond disc makes your wife happy.
A: I have little experience with dental drills (although I have indeed just come from the dentist), but I have written a few milling programs on a CNC mill, so that I think: I can answer this one!
It's not entirely clear to me whether milling or grinding is generally used in dental treatment. But the considerations are similar.
Let's start with milling:
A milling cutter cuts chips from the workpiece (in this case, the tooth). At the very least, the cutting edge should be harder than the material being cut, otherwise it will not survive for long.
In milling, there are two main parameters that affect the process: The speed of the cutting edge and the "feed" of the cutter.

*

*The speed of the cutting edge (the so-called cutting speed) can be
easily calculated if you know the diameter of the cutter and its
rotational speed: v = Pi * D * f. Of course, this only applies to
the outer edge of the cutter. There are milling cutters that have
the cutting edges at the bottom (similar to a metal drill). Then the
cutting speed at the edge is like according to the formula - and it
becomes smaller and smaller towards the inside. In the middle it is
theoretically zero.  However, one tries to avoid this    situation
if possible. The cutting speed is therefore the speed with which the
cutting edge is moved through the material. It can be  varied via
the cutter diameter and the speed of rotation.

*The "feed" is actually about the thickness of the chips: Let's say a cutter with one cutting edge rotates 100 times per second and is moved into the
material at 1 mm per second: Then each chip is 0.01 mm thick. If the
cutter had 2 cutting edges, it would cut chips 0.005mm thick,
because then a cutting edge would be fed through the material twice
as often. The feed rate is always what you have to set for CNC
milling. There it is specified in mm/min. If you want Chips with thickness d, your tool has n cutting edges and is turning with f turns per second, then the feedrate is d * n * f.

There are a few different angles at which the cutting edge of the milling cutter can be set. Nowadays, you just buy a milling-tool for a certain material, where the manufacturer has it all worked out. That is why I know almost nothing about that.
Now to the question of why dental drills turn so fast:
I am not an expert in the field of dental treatment, so as a physicist I would just like to make an educated guess:
I believe that the high rotational speed is about small forces that are supposed to act on the tool, the handle and, above all, the dentist's hand.
The feed is literally in the dentist's hand. He moves the tool with his hand.
I know from experience that the forces on the milling cutter can be very high if the material removal rate is too high (that is the chips are to thick).
(I still remember how my milling machine rattled when I once accidentally removed too much material at once).
The finer the chips you cut, the lower the forces acting on the cutting edge and therefore the whole tool.
In addition, the high rotation frequency means that vibrations from the milling are also transmitted to the handle at this frequency.
(Is that ultrasound then?)
I assume that the dentist is less disturbed by this when working.
When I think about it, the laws of grinding are very similar. The only difference is that the material is not cut, but rather "scratched out" with small particles.
Optimizing the milling process is always a trial and error process. You try out which cutting speed works with which feed rate for a certain material.
And of one thing I am sure: they do it because it works better!
Hope I could help.
*** Translated with www.DeepL.com/Translator (free version) ***
