Her lawyer, Kevin Lawlor, declined to comment.
The decision was met mostly with celebration on social media, in a majority-black country where profound inequality coexists with memories of an apartheid system that institutionalized racial separation and oppression.
But many white people criticized the prosecution and sentence as highlighting what they called a double-standard, because black people — including politicians — have not been penalized for insults and threats of violence to whites.
Ms. Momberg was prosecuted under a long-established legal principle, crimen injuria, which involves harming a person’s dignity. She was convicted in November of four counts of crimen injuria, one for each of the police officers she abused verbally.
The concept has been applied mostly in civil suits. When used in criminal cases, it often includes physical harm. The concept has rarely been used to address racist language.
“Past racists who have come to court have been given very small fines and have been treated very leniently, and it didn’t serve any deterrence,” said Neeshan Balton, executive director of the Ahmed Kathrada Foundation, an anti-racism group. “I think this will be a deterrent.”
The government has drafted a bill specifically to outlaw hate speech, prompting a fierce debate about the limits of free speech in a democratic society.
The Momberg case sets a precedent that could result in “an increasing number of people, across the political spectrum, being jailed,” warned Michael Morris, head of media at the Institute of Race Relations, which advocates free-market economics, an end to race-based policies to benefit nonwhites, and the rights of property owners, who are primarily white.
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The proposed hate speech law, which would include civil and criminal penalties, “would be a backward step for civil liberties in democratic South Africa,” he said.
But Mr. Balton said that he welcomed the bill, and that the debate over it “will bring about a national discourse on what are the kinds of sanctions that are appropriate for racists, and particularly racists who show no remorse for their actions.”
The concept of criminalizing speech, however offensive, sounds discordant to many people in the United States, where expression that does not physically endanger people is generally protected by the First Amendment.
But many Western democracies, including Canada, Britain, France and Germany, have laws that carry criminal penalties for speech intended to humiliate or incite hatred against people based on race, religion, sex or other factors.
The epithet is derived from an Arabic term for non-Muslims, and medieval Arab traders applied it to the people they encountered while sailing down the east coast of Africa. Europeans who arrived later adopted the term and used it for blacks generally.
The video of Ms. Momberg became a sensation partly for the ferocity of her rant, which lasted for several minutes, and included her yelling at officers, using the explosive epithet 48 times, and making explicit her animus toward black people.
“I hate every one of them,” she said. “If I see a kaffir I will drive him over. If I have a gun, I will shoot everybody.”
She insisted repeatedly that she would not interact with black officers, using the epithet to describe them.
A white police officer can be seen trying unsuccessfully to calm her, saying quietly, “I’m not going to allow you to insult my colleagues like that.”
Her lawyers have said that Ms. Momberg’s language reflected her emotional state after being robbed and waiting for help, rather than hard-core racism. But testimony against her indicated that she had used racist language and expressed racist views in other contexts.
Magistrate Raghoonandan said she did not believe that the defendant was remorseful.
At Ms. Momberg’s sentencing hearing last week, her lawyer, Mr. Lawlor, argued that she should be given probation and psychiatric treatment, rather than prison. Last year, another court, the Equality Court, ruled her behavior offensive and fined her 100,000 rand, or about $8,500.