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I sense some confusion in your ideas, let's try to set things straight.

a planet 100 times the size of earth, assuming everything is similar to earth, 1 day (1 rotation) is 24 hours (therefore the planet will be spinning faster than earth?)

Setting aside the plausibility of such a planet, Earth does a complete rotation around itself in 24 hours. This planet does a complete rotation around itself in 24 hours. The rotational velocity is the same for both.

Would there still be 24 time zones, one for each hour?

In principle yes, but it can also be that, due to the larger linear distances between the zone extremes, half hour time zones can be used. Don't forget time zones are just a convention, in the past each city had its own time.

But trying to imagine someone getting up in China the same time someone gets up on the west coast of America is getting to me,

This is blatantly false: if you look at the official time zones on Earth,

You see that while China is +8 UTC, America west coast is -8 UTC. This means 16 hours difference.

If the planet rotates at the same rate as Earth, it'll have the same difference in sunrise, sunset, noon and midnight times for a given number of degrees of longitude, so will have the same "number of time zones" as Earth. These zones will naturally be much wider than those on Earth, but they'll work just the same way -- including needing a "date line" so you don't lose a day if you circumnavigate to the west (as Magellan's crew did).

However: The contiguous United States has four time zones for a width of around 3000 miles. If the United States were, instead, 300,000 miles wide, there might well be three hundred time zones. Why?

Time zones originally came from railroads. Before the 1860s, each town would set its clocks based on (usually) local noon, because it's easy to measure. But with railroads and telegraphs, it was necessary to know what time the train would arrive and depart -- which meant it was necessary, as well, to know what time it was in Tempe when you were leaving Kansas City. Having only four zones for the whole nation meant you could know that Tempe, Sheridan, and Butte had their clocks set the same -- and telegraphy made this actually practical, by allowing near-instantaneous transmission of time synchronizing signals.

But trains can only travel a few hundred miles in a day (at least with early steam technology), so there's no need to have time zones as coarse as 75,000 miles across -- there might well be "minute" zones, and they'd still be wider than the "hour" zones we have on Earth.

"Timezone" are all "subjective"! It was first created by Scottish-born Canadian Sir Sandford Fleming in 1876. It's all for us-human-being's convenience!

The very fact that the timezone lines on Earth are all crooked at many places prove it!

The main part of Greenland lay across 4 timezones! But they don't like the idea and make the whole chunk of land under 1 timezone!

And if you across the sea from the Northwest coast to Quttinirpaaq National Park, you had "jumped" across "TWO" timezones!

And certain countries have "Daylight Saving Time"! Which means in the same timezone, the time is different in Summer and Winter time!

That further proved that "time and timezone" are all for "OUR" convenience!

So to come back to your question, you could have "as many timezones as you want"!

You can even divide the globe into "15-minute-timezones" if you so wish!

And that might be a better idea since your planet is SO~ big!

Another way to approach the problem:

"Suppose humans were 1/10th their current size. Would that require any change to time zones?"

No, not really.

As others have said here, time zones aren't a natural phenomenon, so there's no reason to make a change unless we wanted one.

It depends what you want out of your timezones. If we consider an idealized Earth time-zone, it is 1 hour 'wide', meaning that at each edge of the zone, sundials will disagree by a difference of 1 hour.

If then we consider what it means for the sundials to differ by that amount, we can realize that it means they are resting at different angles (since the Earth's surface is roughly spherical). The exact angle just so happens to be 1/24th of the way around the Earth, or 360 * 1/24 = 15 degrees. So, our ideal time zone is 15 degrees wide.

Now, let us change the size of the planet. Since a circle of any size still encompasses 360 degrees, a 1-hour time zone would still cover 15 degrees.

So, in conclusion, the width of the time zones are determined more by the time difference than anything else, and as other answers have suggested, the time difference is a purely social/political/economical decision.

There is no reason to have 12 (24) hours per day other than "because".

In ancient Babylonia, people used a sexagesimal (base-6, not base-10) counting system. For... whatever reason. Which means that everything, length, weight, and time was measured and accounted for in multiples of 6.

So for example, you would have us, which was 60 ells, and nus and sar, which were multiples of that (sar would be 1800 ells). Very queer, but I guess if you count base-6 then it feels quite normal.

It so happens that 10 is not a multiple of 6, but 12 is. Hence the day (the complete day, including night!) had 12 danna. This, somehow, nobody knows how, remained until some 2,000-3,000 years later, the Italians started counting not at midnight, but when the sun rises, and they thought that a two-hour period was too coarse over the (half) day, so they split the danna in two, giving 24 hours on what's called the "big clock".

Some hundred years later, people found it easier, and cheaper, to use the "little clock" where you no longer have 24 hours, but 12 + 12 hours instead, reusing the same dial on the exceedingly difficult to manufacture and extremely expensive single mechanical clock they could (maybe, possibly, if lucky) afford.

So, it all boils down to what you count in, and what you are comfortable with. Your planet is twice or twenty times or a hundred times the size? Can still count 12 hours, or 120 hours. Or, while you are at it, why not precisely 1,000 hours which would work much better with SI units.

I'd consider "What about gravity?" a much more challenging question if your planet is that big. A hundred times the circumference means it has ten thousand times the gravity (give or take some, might be somewhat more or less, depending on density, the general figure remains though). Does it rotate so fast that centrifugal force at least partly compensates for stuff weighting 10,000 times as much? That'd be fun watching stars in the sky :-)