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Abanar vs. balançar

When describing the action to wag in Portuguese, particularly regarding a tail, the choice between abanar and balançar depends on the speed and intent of the movement. Generally, abanar implies energy and excitement, while balançar implies a rhythmic swaying motion.

Abanar

A2
This verb describes a rapid, vigorous shaking or fanning motion. It is the most common word used when a dog wags its tail out of happiness or excitement. The movement associated with abanar is usually fast and energetic.
O cão abana a cauda sempre que o dono chega a casa.
(The dog wags its tail whenever the owner comes home.)
O cachorrinho ficou tão contente que começou a abana o rabo furiosamente.
(The puppy was so happy that it started to wag its tail furiously.)
É um sinal de amizade quando eles abanam a cauda.
(It is a sign of friendship when they wag their tails.)

Balançar

B1
This verb describes a swaying, swinging, or rocking motion, similar to a pendulum or a swing. When referring to a tail, balançar implies a slower, rhythmic side-to-side sweep rather than a vibration. It is often used for other animals like cats, horses, or lions, or for dogs moving lazily.
O gato balança a cauda lentamente enquanto observa a presa.
(The cat sways its tail slowly while watching the prey.)
Para afastar as moscas, o cavalo balança a cauda de um lado para o outro.
(To ward off flies, the horse swings its tail from one side to the other.)
O leão balançou a cauda preguiçosamente enquanto dormia.
(The lion swayed its tail lazily while sleeping.)

Summary

In short, use abanar when the wagging is fast, energetic, and typically related to happiness (like fanning). Use balançar when the movement is a slower, wider side-to-side sweep (like a pendulum swinging).