How could any frame of reference be inertial? The image below shows that a bystander watching the merry-go-round is in an inertial frame of reference. However, to nitpick, wouldn't the observer still be accelerating because it's on Earth?

 A: In newtonian mechanics, inertial frames are an equivalence class. They can be defined as frames where Newton's laws are valid.
If you can find one inertial frame, then you automatically get an infinite number of other such frames by trying all galilean transformations from the first one.
There is, however, no true inertial frame in practice. The best we can do is to ask, for a given frame of reference, whether or not treating it as an inertial frame is a good approximation.
For instance, if you're studying the oscillations of a pendulum over the span of a minute or two, the terrestrial frame is a good inertial frame, as is taught (more and more silently) in high school.
But if you're studying the oscillations of a large pendulum for hours or days, then treating that same frame as an inertial frame will give bad results than don't match reality (see Foucault pendulum), because you can't neglect Earth's rotation over such an extended period of time.
In practice, the best approximation for an inertial frame that we have is the Copernicus one. But for most usecases, it's cumbersome to use, so we have a hierarchy of frames that are less and less inertial, but that can be easier to use:

*

*Copernicus frame

*Heliocentric frame

*Geocentric frame

*Terrestrial frame

*local frame

