بساط التمرين نظيف، والثقل اليدوي جاهز اليوم.

Because بساط التمرين is an iḍāfa construction, often called a construct phrase.

In an iḍāfa:

• the first noun usually does not take الـ
• the second noun tells you what kind of thing it is or what it belongs to
• the whole phrase can still be definite

So:

• بساط تمرين = an exercise mat
• بساط التمرين = the exercise mat

Even without الـ on بساط, the whole phrase is definite because the second noun التمرين is definite.

It is the second noun in the iḍāfa.

Literally, بساط التمرين is something like the mat of the exercise. In natural English, we say exercise mat.

This is a very common Arabic pattern:

• باب البيت = the door of the house
• كتاب الطالب = the student's book
• بساط التمرين = the exercise mat

Grammatically, the second noun in an iḍāfa is in the genitive case in full formal Arabic.

Because نظيف here is not just an adjective attached to the noun. It is the predicate of the sentence, meaning is clean.

So:

• بساط التمرين نظيف = The exercise mat is clean

But if you wanted clean to directly describe the noun inside one noun phrase, you would use:

• بساط التمرين النظيف = the clean exercise mat

That is the key difference:

• نظيف = predicate, so usually indefinite
• النظيف = attributive adjective modifying a definite noun, so it must also be definite

Because in Arabic, the present tense often has no written or spoken copula in simple nominal sentences.

So Arabic says:

• بساط التمرين نظيف
• literally: the exercise mat clean
• natural English: The exercise mat is clean

The same happens in the second clause:

• الثقل اليدوي جاهز اليوم
• The hand weight is ready today

If you want was, will be, and so on, Arabic usually uses words like:

• كان = was
• سيكون = will be

Here, اليدوي is an adjective, not the second noun of an iḍāfa.

So:

• الثقل = the weight
• اليدوي = manual / hand / hand-held
• الثقل اليدوي = the hand weight or the dumbbell / hand weight

A good clue is that اليدوي agrees with الثقل like an adjective:

• both are definite
• both are singular
• both are masculine

That is different from بساط التمرين, where the second word is a noun in an iḍāfa.

Because they have different jobs in the sentence.

• اليدوي is an adjective modifying الثقل
• جاهز is the predicate, meaning is ready

So:

• الثقل اليدوي = the hand weight
• الثقل اليدوي جاهز = the hand weight is ready

When an adjective directly modifies a definite noun, it also becomes definite:

• الثقل اليدوي

But the predicate in a nominal sentence is usually indefinite:

• جاهز

The و means and.

In Arabic, this wa- is usually written attached to the following word, so:

• والثقل = and the weight

This is completely normal in Arabic spelling. Other short particles are often attached this way too.

It is one written sentence, but grammatically it contains two nominal clauses joined by و.

Clause 1:

• بساط التمرين = subject/topic
• نظيف = predicate

Clause 2:

• الثقل اليدوي = subject/topic
• جاهز = predicate
• اليوم = time expression

So the structure is basically:

• The exercise mat is clean, and the hand weight is ready today.

اليوم means today, and here it works as a time expression.

In this sentence, it most naturally applies to the second clause:

• والثقل اليدوي جاهز اليوم
• and the hand weight is ready today

Because of its position, a learner would normally understand today as connected mainly to جاهز.

If you wanted today to feel more clearly connected to the whole sentence, you could move it earlier, for example:

• اليوم بساط التمرين نظيف، والثقل اليدوي جاهز
• Today, the exercise mat is clean, and the hand weight is ready

Arabic word order is fairly flexible, but this order is a very natural and straightforward one for learners.

The basic pattern here is:

• subject + predicate

So:

• بساط التمرين نظيف
• الثقل اليدوي جاهز اليوم

You can move things around for emphasis, especially time expressions like اليوم, but for clear standard Arabic, the given order is excellent.

For example:

• اليوم الثقل اليدوي جاهز
• Today the hand weight is ready

That emphasizes today more strongly.

A rough pronunciation is:

bisāṭ at-tamrīn naẓīf, wa-th-thiqal al-yadawī jāhiz al-yawm

A few useful pronunciation notes:

• الـ before ت in التمرين is pronounced with assimilation:
  at-tamrīn, not al-tamrīn

• الـ before ث in الثقل also assimilates:
  ath-thiqal

• ث sounds like th in think

• ظ in نظيف is an emphatic sound, often approximated by English speakers as a heavy z

• ج in MSA is usually pronounced like j in judge

Also, in normal speech, learners often hear or say the sentence without full case endings.

In a fully inflected formal reading, you could write:

بساطُ التمرينِ نظيفٌ، والثقلُ اليدويُّ جاهزٌ اليومَ.

Why these endings?

• بساطُ: nominative, because it is the subject/topic of the first clause
• التمرينِ: genitive, because it is the second noun in an iḍāfa
• نظيفٌ: nominative, because it is the predicate
• الثقلُ: nominative, subject/topic of the second clause
• اليدويُّ: nominative adjective matching الثقل
• جاهزٌ: nominative predicate
• اليومَ: accusative as an adverbial expression of time

In everyday reading, these final vowels are often omitted, but they matter in fully formal MSA grammar.