This is for the history buffs among you... numismatic and American

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braddick

The liberty cap and pole are symbols of freedom and resistance to tyranny.

The liberty cap and pole originated in 44 BCE after the assassination of Julius Caesar by Roman senators. The senators, known as the Liberatores, carried a Phrygian cap on a spear to symbolize that the Roman people were free from Caesar's rule.
American colonists adopted the liberty cap and pole as a symbol of their fight against British rule. The Sons of Liberty would raise liberty poles in colonial towns and hold rallies around them. In 1775, British soldiers cut down a liberty pole in Concord, Massachusetts, which led to the "shot heard 'round the world"

(Not being a know-it-all.)

lermish

Lots of other countries use the phrygian cap on their coinage also.

A small sample:

BillJones

The Libertas Americanas medal inspired these early copper designs.

yosclimber

More on what @braddick posted.

In Ancient Rome, a slave was freed in a ceremony in which a praetor touched the slave with a rod called a vindicta and pronounced him to be free. The slave's head was shaved and a pileus was placed upon it. Both the vindicta and the cap were considered symbols of Libertas, the goddess representing liberty.

https://en.wikipedia.org/wiki/Pileus_(hat)

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Sapyx

Ancient depictions of Libertas (Liberty) on Roman coinage often use the cap, though she is never shown wearing it, since she herself was never the slave. The cap does not belong to her, but rather to the person being freed; she is the one who awards the cap to the freed person. So she is often shown holding out the cap in one hand.

Denarius of Nerva.

Denarius of Elagabalus.

This Denarius of the Roman Republic, 76 BC, depicts the head of Libertas with the cap next to it; a clear precursor to early American designs.