Компьютерная мышь удобна, когда нужно быстро двигаться по экрану.

In Russian, every noun has a fixed grammatical gender that does not change with meaning or context.

• The word мышь (mouse, the animal) is historically feminine, and it keeps that gender in all uses.
• When Russian started using мышь for the computer device, it simply reused the existing word with its existing gender.

So:

• компьютерная мышь → feminine adjective + feminine noun
• мышь удобна → short-form adjective in feminine

You must treat a computer mouse as она (she), never as neuter or masculine:

• Где моя мышь? Она не работает. – Where is my mouse? It’s not working.

Russian has two main types of adjective forms: full (long) and short.

• Full forms: удобный / удобная / удобное / удобные
• Short forms: удобен / удобна / удобно / удобны

1. Before the noun (attribute), you normally use the full form:

• удобная мышь – a convenient mouse

2. After the noun, as a predicate, the short form is very common:

• Мышь удобна. – The mouse is convenient.

In your sentence, удобна is a short-form adjective used as a predicate:

• Компьютерная мышь удобна, ... – The computer mouse is convenient when...

You could also say Компьютерная мышь удобная, когда..., but:

• удобна sounds like a neutral statement of fact.
• удобная after the noun can add a slightly more descriptive or contrastive feel (e.g. “this mouse is one of the convenient ones”), and is less neutral stylistically here.

Grammatically, there is no explicit subject here. This is an impersonal construction.

• нужно двигаться literally: “it is necessary to move”
• There is no я / ты / он / она / мы / вы / они in the sentence.

In English we naturally supply you or one:

• “when you need to move quickly on the screen”
• “when it is necessary to move quickly on the screen”

Russian often leaves this “generic person” unspoken. If you wanted to specify who, you would usually put that in the dative:

• Когда вам нужно быстро двигаться по экрану... – when you (formal/plural) need to move quickly on the screen
• Когда мне нужно быстро двигаться по экрану... – when I need to move quickly on the screen

But in the original, it’s general and impersonal: “when (one) needs to move quickly on the screen”.

Both нужно and надо can express necessity and both often translate as “need to / have to / must”.

In the construction with an infinitive:

• нужно двигаться
• надо двигаться

the meaning is almost the same. The main differences:

• Style:

  • нужно is a bit more neutral/standard and can sound slightly more formal or written.
  • надо is very common in everyday speech and sounds a bit more colloquial.

• Grammar flexibility:

  • нужно can also behave like a short-form adjective that agrees with a noun:
    
    • Мне нужен компьютер. – I need a computer.
    • Ей нужны деньги. – She needs money.
  • надо does not change form.

In your sentence, using нужно is natural and slightly more neutral in tone than надо, but надо would also be understood and acceptable in many contexts:

• Компьютерная мышь удобна, когда надо быстро двигаться по экрану.

двигать and двигаться are different verbs:

• двигать = to move something (transitive)

  • двигать стул – to move a chair
  • двигать мышь – to move the mouse

• двигаться = to move (oneself), to be in motion (intransitive, reflexive)

  • Я двигаюсь. – I am moving.
  • Курсор двигается по экрану. – The cursor moves on the screen.

In your sentence:

• когда нужно быстро двигаться по экрану

the focus is on the motion itself on the screen, not on you physically moving the mouse object. It’s closer to “when you need to be moving quickly on the screen” or “when you need to move around quickly on the screen.”

If you wanted to emphasize moving the mouse device, you’d use двигать with a direct object:

• Когда нужно быстро двигать мышь по экрану, ... – when you need to move the mouse quickly across the screen...

Russian aspect contrasts process / repeated action (imperfective) with single, completed action / change (perfective).

• двигаться (imperfective) – to move (be in motion, process, repeated action)
• двинуться (perfective) – to move once, to start moving, to make a single move

Your sentence describes a general situation and typical use:

• Компьютерная мышь удобна, когда нужно быстро двигаться по экрану.

This means: “The mouse is convenient in situations where you (often/typically) need to move quickly on the screen.” That’s a general, ongoing type of action, so the imperfective is correct.

If you said когда нужно быстро двинуться по экрану, it would sound like a specific, one-time quick movement (“when you need to make one quick move across the screen”), which is not the general idea here.

The part starting with когда is a subordinate clause (a dependent clause of time/condition):

• когда нужно быстро двигаться по экрану – when (it’s) necessary to move quickly on the screen

Russian normally separates a main clause and a subordinate clause with a comma when they are linked by conjunctions such as когда, потому что, если, хотя, etc.

Patterns:

• Главное предложение, когда придаточное.
  Компьютерная мышь удобна, когда нужно быстро двигаться по экрану.

• Or the reverse order:
  Когда нужно быстро двигаться по экрану, компьютерная мышь удобна.

In both orders, you keep the comma between the main and subordinate clauses.

Several points are involved: the preposition, the case, and the meaning.

1. Preposition and case

With the meaning “to move over / along / across a surface,” Russian uses:

• двигаться по чему? – to move across/along something

The preposition по here requires the dative case:

• экран (nominative)
• экрану (dative)

So:

• по экрану – across the screen

по экран is incorrect because по does not take the accusative in this meaning.

2. Meaning vs. other options

• двигаться по экрану – to move around/across the whole screen (motion over its surface)
• двигаться на экране – to move on the screen (emphasizes being displayed and moving there; common about images, objects in a game, etc.)

For a cursor or for general motion over the screen area, по экрану is very natural:

• Курсор двигается по экрану. – The cursor moves around the screen.

The basic meaning is stable, but Russian allows flexible word order with slight changes in emphasis.

All of these are grammatically correct:

1. Компьютерная мышь удобна, когда нужно быстро двигаться по экрану.
   – Neutral: “The computer mouse is convenient when you need to move quickly on the screen.”

2. Когда нужно быстро двигаться по экрану, компьютерная мышь удобна.
   – Puts more emphasis on the condition; like “When you need to move quickly on the screen, the computer mouse is convenient.”

3. Компьютерная мышь удобна, когда быстро нужно двигаться по экрану.
   – Slightly shifts focus so that быстро modifies нужно more strongly: “when it’s quickly that you need to move on the screen” (still very similar in practice).

The core restrictions:

• Компьютерная мышь удобна must stay as a coherent main clause.
• The когда-clause must remain together as its own block.
• You keep the comma between the main clause and the когда-clause.

• быстрый is an adjective: it describes a noun.

  • быстрая мышь – a fast/quick mouse
  • быстрый компьютер – a fast computer

• быстро is an adverb: it describes a verb (an action).

  • двигаться быстро – to move quickly
  • Он быстро работает. – He works quickly.

In the sentence:

• нужно быстро двигаться по экрану

быстро modifies the verb двигаться (how to move? quickly), so the adverb form is required. An adjective form быстрый cannot be used there because no noun follows it to be described.