The mantle of the vice presidency was passed yesterday from Nelson Aldrich Rockefeller to Walter Frederick Mondale in a brief, simple ceremony.

For Rockefeller, who had foresworn the office and then occupied it in a time of crisis, the ceremony on the platform over the east steps of the Capitol meant a quick change to the business life.

In fact, according to a Rockefeller spokesman, the former Vice President was in a New York business meeting at 3 p.m. yesterday, about three hours after Mondale was sworn in as the 42d Vice president of the United States.

For Mondale, 49, the oath he took on a family Bible meant an opportunity to make the vice presidnecy, for the first time, a significant national office.

But before setting about that task, the new Vice President busied himself with more ceremony, the parade and the parties that marked his entry into the second-highest - at least protocol - offfice in the land.

The two men began their days differently.

Mondale's first activity was to feed the cold and the hungry - reporters. About 8:30 a.m. he stepped outside his home in the Cleveland Park section of Washington with a paper plate of steaming breakfast rolls for a small group of reporters and photographers who had gathered outside.

About 15 minutes later, he and his wife, Joan, emerged from the house arm in arm and went to a pre-inauguration service at the First Baptist Church of Washington.

One of the three ministers conducting the services was Joan Mondale's father, Dr. John Maxwell Adams of Afton, Minn., a Presbyterian. Those in attendance included President-elect Jimmy Carter and his family and various officials of the incoming administration.

Following the service, the Carters and the Mondales traveled in motor-cades to the Blair House, the official visitors' residence. They stayed there for a half hour before going across the street to the White House for coffee with President Ford and Vice President Rockefeller.

Rockefeller started his day by eating - at a White House breakfast given for the outgoing Vice President and Cabinet by President Ford.

After breakfast, Rockefeller went to his office in Room 275 of the Executive Office Building. He stayed there until it was time to return to the White House for the coffee session with Ford and the Carters.

At 11:15 a.m., a motorcade carrying the principals in the inaugural left for the Capitol. Forty-five minutes later, Mondale put his left hand on the Bible, rasied his right hand, and was sworn into office by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.),

Rockefeller sat attentively through the whole affair, alternately smiling and displaying solemnity. Afterward he and his wife, Happy, accompanied the Fords on a 20-minute helicopter tour of Washington, and then on a brief trip to Andrew Air Force Base - the scene of the Ford-Rockefeller departure from the capital.

Rockefeller arrived at La Guardia Airport in New York at 2:20 p.m. He immediately left the airport to keep the 3 p.m. business appointment in his Manhattan office in Rockefeller Center.

Rockefeller would spend the night in his Fifth Avenue apartment, according to his former spokesman, John H. Mulliken Jr. But before retiring for the day he would attend a cocktail party given in his honor by his brother, David, president of the Chase Manhattan Bank.

Back in Washington, Mondale was caught up in the parade and parties. So exuberant was he that, at one point in the parade, at the corner of 15th Street and Pennsylvania Avenue, he left his limousine to shake hands and walk among people. Carter was already on foot.

Mondale said he planned to attend six of the seven inaugural parties. He planned to end the night with party goers from his native state of Minnesota at the Shoreham Hotel.

In other corners of Washington, specifically in Mondale's old office in the Russell Senate Office Building, flustered staff aides were trying to cope with the change.

A telephone rang in the office at about 4 p.m.

"Sen. Mondale's office," the aide said. Embarrassment. Then laughter. "I mean, Sen. Wendell Anderson's office Sen. Mondale's not here. Uh, he's the Vice President - Mondale, I mean," said the aide.

She finally collected herself. "I work for Anderson (the Minnesota Democrat who replaced Mondale in the Senate). If you want Sen. Mondale, I mean the Vice President, you have to call the Vice President's office," the aide said.

The call was made.

"Office of the Vice President," a staffer answered.

"The new one or the old one?" she was asked.

"The new one," she said cheerfully. "The old one's gone."