Waaaaaaaaaaaaaaaaay back then when firearms were first invented, they fired large balls. Now the norm is .22ish caliber rifles. Why is it that the bullets got smaller and smaller?
When black powder was the only gun powder, in order to get the required energy out of said projectile, it had to be large and heavy, like the .75 caliber brown bess
nowadays, with modern smokeless powder, a smaller lighter projectile can be moved many times faster, which yields similar (or more in some instances) than the previous heavy slow projectile
energy is determined by multiplying mass (the amount of matter or "stuff" in something) times the velocity squared
Energy = Mass*(Velocity^2)
E=mv^2
if we take a 545 grain .71 caliber ball over 100 grains of black powder (British Army Brown Bess load), you would get around 1000fps, you get about 1210 foot pounds of muzzle energy
alternatively,the M16 load, a 55 grain .224 caliber bullet pushed to 3110 feet per second yields 1181 ft/lbs
those are similar muzzle energies
but they are not the only factors at play here
momentum is the measure of how much energy it takes to get something moving (or stop its movement)
it is calculated by multiplying velocity times mass
so 545 grains * 1000 fps gives us a momentum (p) of 545,000
while 55 grains * 3110 fps = P = 171,050
so now we know that the large ball has more momentum and we can then summarize that it takes more energy to get it moving
that then brings us to newtons third law of motion: For every action, there is an equal and opposite reaction.
so if the brown bess takes (X) amount of energy and applied it to the heavy ball, then the third law says that the heavy ball will be applying the exact equal energy (X) back to the rifle system (which includes the shooter) which translates into recoil
the M16 bullet (with a lower momentum) requires less energy to move it and thus applies that same lower amount back to the rifle and shooter
simply put, we get less recoil for the same amount of muzzle energy
also, and not AS physics related, 180 rounds is a standard combat ammo load, and 180 .71 caliber lead balls weighs over 14 lbs (not including powder) and 180 rounds of 5.56 weighs just shy of 5 lbs