What if inertial and gravitational mass were different?

Question

It's well known and heavily documented that gravitational and inertial mass are identical.
This has been experimentally tested to many digits of precision.
But nothing I've seen ever describes how they could be different (e.g. linear or non-linear relationship) or what the universe would be like if they were significantly different.
Ignoring both the quantum world and relativity, and sticking with Newtonian mechanics to simplify things, what are some obvious specific examples of how we would see the world operate differently?

gandalf61 · Answer

If the relationship between inertial mass and gravitational mass were not the same for all fundamental particles then one consequence would be that the acceleration due to gravity would depend on what an object was made of. So a hammer and a feather really would fall at different speeds in a vacuum.
In fact, it is only a hypothesis that antimatter particles have the same gravitational properties as their normal matter counterparts - we do not know this for certain. There are ongoing experiments at CERN that are testing this hypothesis - see this Wikipedia article for more details.

What if inertial and gravitational mass were different?

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