A whip is deemed to be an instrument of dominance, torture, and persecution. Many expressions, such as "crack the whip" and "whip into shape" reflect this connotation.
In Animal Farm, Mr. Jones and his men use whips to control, punish and torture the animals. It has become a symbol of man's abuse and exploitation and, as such, is a much-reviled object. It is one of the first things the animals destroy after the Rebellion.
The reins, the halters, the blinkers, the degrading nosebags, were thrown on to the rubbish fire which was burning in the yard. So were the whips. All the animals capered with joy when they saw the whips going up in flames.
The animals are ecstatic because they believe that they would never have to endure the pain inflicted by this terrible instrument. Man's dominance has ceased, and they now have their destiny in their hands. There will, they believe, now ensue a period of equality and mutual respect between animals. They will be forever free. Their fear of torture is now something of the past.
The animals are shocked and dismayed, however, when they see Napoleon walk upright with a whip in his trotter in chapter ten.
...out came Napoleon himself, majestically upright, casting haughty glances from side to side, and with his dogs gambolling round him.
He carried a whip in his trotter.
There was a deadly silence. Amazed, terrified, huddling together, the animals watched the long line of pigs march slowly round the yard.
At this moment the animals know, in some way, that things have taken a dramatic change. Some of them who might want to protest are stifled before they even begin because all the sheep start repeatedly shouting: "Four legs good, two legs BETTER!"
The final expression of the pigs' dominance and control is contained in a paradoxical new single commandment written on the side of the big barn. Benjamin reads the rule to Clover:
All animals are equal but some animals are more equal than others
Deep down the animals now realize that the pigs are their new masters. After this, they accept without question whatever the pigs do, even when it involves adopting human traits and purchasing luxuries and tools typically reserved for human consumption and use.
Life on the farm has gone full circle and, in the closing paragraphs, the animals can no longer distinguish between pig and man. Their former abusers have been replaced by a new authority in the form of the pigs which, ironically, leaves them worse off than they have ever been.
The revolution has, for all intents and purposes, been a failure for the animals but a massive success for the pigs.