Мяч катится по полу.

Because мяч is the subject of the sentence, so it is in the nominative case.

• мяч = ball
• In Мяч катится по полу, the ball is the thing doing the action

So this is the normal dictionary form of the noun.

Катится comes from the infinitive катиться, which means to roll.

In this sentence, катится is:

• 3rd person singular
• present tense
• used with он / она / оно-type subjects, including nouns like мяч

So:

• мяч катится = the ball rolls / is rolling

The -ся ending is very common in Russian. Here it is part of the verb катиться, which means to roll by itself / be rolling.

This is different from катить, which usually means to roll something.

Compare:

• Мяч катится. = The ball is rolling.
• Он катит мяч. = He is rolling the ball.

So -ся here helps show that the subject is undergoing the movement itself, not causing something else to move.

Because Russian uses two different verbs here:

• катить = to roll something, to make something roll
• катиться = to roll, to be rolling

So:

• Мяч катится is correct for the ball is rolling
• Мяч катит would sound wrong in this meaning, because катит usually needs an object, like катит мяч

Полу is the dative singular of пол meaning floor.

It appears after the preposition по, which often takes the dative case when talking about movement along, over, or across a surface.

So:

• пол = floor
• по полу = along the floor / across the floor / on the floor as a path of movement

That is why the sentence uses по полу, not just пол.

This is a very common question.

• на полу = on the floor as a location
• по полу = along/across the floor as the path of movement

Compare:

• Мяч на полу. = The ball is on the floor.
• Мяч катится по полу. = The ball is rolling along the floor.

So in your sentence, по полу is used because the ball is moving.

Катится is pronounced roughly KA-ti-tsa.

A few helpful points:

• the stress is on the first syllable: ка́тится
• in verb endings like -тся, the combination is pronounced approximately like ца

So learners often hear:

• written: катится
• pronounced: ка́тица

This is normal in Russian pronunciation.

A natural pronunciation is roughly:

Мяч ка́тится по полу́.

Helpful stress:

• мяч
• ка́тится
• полу́

Very approximate English-style guide:

myach KA-ti-tsa pa pa-LU

That guide is only approximate, but it can help at first.

Russian has no articles, so there is no separate word for a or the.

That means мяч can mean:

• a ball
• the ball

The exact meaning depends on context.

So Мяч катится по полу could be understood as either:

• A ball is rolling along the floor
• The ball is rolling along the floor

In Russian, the present tense often covers both ideas:

• rolls
• is rolling

So Мяч катится can mean either:

• The ball rolls
• The ball is rolling

In most real situations, context makes it clear that it means is rolling.

Yes. Russian word order is more flexible than English word order.

The neutral order here is:

• Мяч катится по полу.

But you could also say:

• По полу катится мяч.
• Катится мяч по полу.

These versions are still understandable, but the emphasis changes:

• starting with по полу highlights the setting or path
• starting with катится can sound more descriptive or literary

For a basic learner, Мяч катится по полу is the most neutral and safest version.