agitar

To shake or stir something physically (agita bien la pintura) or, figuratively, to stir up unrest or strong feelings (agitar a las masas, agitar el debate). The figurative political sense — inciting or stirring people up — is old and common enough that agitador (agitator) is a standard word for a political rabble-rouser.

• Agita bien la pintura antes de aplicarla. — Shake the paint well before applying it.
• El discurso agitó a la multitud. — The speech stirred up the crowd.
• Sus declaraciones agitaron el debate en redes sociales. — His statements stirred up the debate on social media.

Missing the political/figurative sense and assuming agitar is only physical shaking — in news and political writing, agitar and agitador almost always carry the 'stir up unrest' meaning, not literally shaking something.

• expression "Agitar las aguas" — A common figurative expression meaning to stir up controversy, provoke necessary change, or deliberately disturb a calm or stagnant situation — the Spanish equivalent of English's 'to rock the boat' or 'stir the pot.'