Lutul este pe roata olarului.

A natural breakdown is:

• lutul = the clay
• este = is
• pe = on
• roata = the wheel
• olarului = of the potter / the potter’s

So the structure is basically:

the clay + is + on + the wheel of the potter

Romanian often expresses possession as the X of the Y, where English may prefer the Y’s X.

Because -ul is the Romanian definite article attached to the end of a masculine or neuter noun.

• lut = clay
• lutul = the clay

Unlike English, Romanian usually puts the at the end of the noun instead of before it.

So:

• lut = clay
• lutul = the clay

The basic noun is roată = wheel.

When it becomes definite, Romanian adds the definite article to the noun, and the form changes:

• roată = a wheel / wheel
• roata = the wheel

This is a normal feminine noun pattern. The final -ă changes to -a in the definite singular form.

olarului is the form of olar = potter used after another noun to show possession.

• olar = potter
• olarul = the potter
• olarului = of the potter / the potter’s

This is the genitive form.

So:

• roata olarului literally means the wheel of the potter
• in natural English: the potter’s wheel

The ending -ului is very common for masculine singular nouns in the definite genitive/dative.

That is a very common difference between English and Romanian.

Romanian often uses:

definite possessed noun + definite genitive possessor

So:

• roata olarului = the potter’s wheel
• literally: the wheel of the potter

This is normal Romanian grammar. English and Romanian package possession differently.

Compare:

• cartea profesorului = the teacher’s book
• literally: the book of the teacher

Here pe means on.

So:

• pe masă = on the table
• pe drum = on the road
• pe roata olarului = on the potter’s wheel

You may also learn later that pe has another important use in Romanian: it can mark certain direct objects, especially people. But in this sentence it is simply the normal spatial meaning on.

Yes. That is completely normal.

• este = full form
• e = shorter, very common spoken form

So both are correct:

• Lutul este pe roata olarului.
• Lutul e pe roata olarului.

The version with este may sound a little more careful or formal, while e is very common in everyday speech.

The given order is the most neutral one:

Lutul + este + pe roata olarului

This is a standard subject + verb + place phrase order.

Romanian word order is somewhat flexible, but changes usually add emphasis or sound more literary or marked. For example, you could move the location phrase forward for emphasis, but the neutral sentence is the one you were given.

So for a learner, this is the safest default pattern.

Yes. You may also see roată de olar.

There is a nuance:

• roata olarului = the potter’s wheel, a specific wheel belonging to a specific potter
• roată de olar = a potter’s wheel, the type of object in general

So in your sentence, roata olarului sounds like a particular potter’s wheel, not just the general kind of tool.

A simple learner-friendly guide is:

LOO-tool YES-te peh ROA-ta o-la-ROO-luy

A few useful notes:

• u is like oo in food
• e in este is often pronounced with a y glide at the start: YES-te
• oa in roata is a real Romanian vowel combination, pronounced together
• ui at the end of olarului sounds roughly like ooy / uy

You do not need perfect pronunciation immediately, but it helps to notice that Romanian spelling is fairly regular once you learn the sound patterns.