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What role does air resistance play in the falling speed of lighter objects like feathers compared to heavier ones like hammers in every day situations?

I dont understand about why objects in free fall, such as a feather and a hammer, accelerate at the same rate when dropped from the same height, despite having clearly different masses. Is it that the feather experiences significantly more air resistance than the hammer, which would cause it to fall slower in a real-world situation? It suspect there is concept or deeper understanding of gravitational forces and their interaction with mass that I am missing, any help is greatly appreciated.

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The Newtonian gravitational force (a good approximation for bodies like the Earth and Sun) is

$$F=ma=\frac{GMm}{r^2},$$

so $a=\frac{GM}{r^2}$ regardless of the mass of the falling object.

Is it that the feather experiences significantly more air resistance than the hammer, which would cause it to fall slower in a real-world situation?

Yes. The Apollo astronauts, when they went to the moon, verified on video that a hammer and feather fall at the same rate in a vacuum, even though they fall at different rates in atmosphere. Not that you couldn't do this on Earth in a big vacuum chamber.

controlgroup
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Imagine you drop an iron ball weighing a kilogram and measure its acceleration under gravity.

Then you use a laser to cut a zero-width centimetre-deep groove round its circumference and measure again.

Then you deepen the groove in stages until there is the thinnest possible thread of iron between the hemispheres, and measure again after each cut.

Then you cut away the last remnant of the connection, and measure again.

At which point do the two separate half-kilogram masses suddenly fall at a different acceleration than the single kilogram mass ?

Paul_Pedant
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