I am idly curious whether any significant proportion of a landing plane's momentum is lost through wheel braking vs. everything else like thrust reversers, aero drag, etc?
If I have to pick a plane, let's go with a 737.
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The vast majority of the stopping power on a landing is the wheel brakes. Reverse thrust is a much smaller component, and as it happens is generally not taken credit for in published landing distance performance data. It's just a bonus. The pilot can choose to use reverse or not, and often won't, maybe only deploying them to idle reverse to have available just in case some braking power is lost for some reason.
Aerodynamic drag is significant at first, although still way less than wheel brakes, but quickly declines as speed comes down, whereas wheel brake power (as in, what you feel as deceleration, not so much actual mathematical energy conversion) is relatively constant all the way to being stopped.
Brakes on airliners and generally split into two separate circuits on each gear, leaving half braking if a sub-system fails. If that happens, landing distance goes way up.
Then there's anti-skid (ABS in a car). Anti-skid is the only thing that allows the pilot to use maximum braking. Without anti-skid, going hard on the brakes will likely lock wheels and blow tires, because airliner brakes are like truck airbrakes, with no feedback at the pedals, just spring pressure, and you can only modulate them based on your sensation of deceleration of the plane.
So, the large majority of an airliner's stopping power is in the brake system, with the anti-skid system making it possible to exploit all of the potential braking power.
Not much, as planes will never carry large heavy wheels into the air. The concept could be tested with models. Some energy will be required to overcome the angular inertia of the wheel.
In olden times, this was known as a "flywheel". This stored energy can be utilized, for example, to keep a piston engine turning smoothly between powerstrokes.
But with aircraft, weight savings is paramount. To scale, any energy going into spinning up wheels on landing is miniscule compared to the kinetic energy of the aircraft. And while we are at it, a bit of energy also goes into the "chirp" on touchdown from frictional heating, also found from braking.