That nebulous notion the policitians call "momentum" came to life here today as more than 10,000 people jammed a downtown square to shout approval for Sen. Edward M. Kennedy (D-Mass.) and his reborn presidential campaign.

The noon crowd, filling every inch of sidewalk and grass on Mellon Square and spilling over into four adjacent avenues, cheered robustly as Kennedy taunted President Carter for failing to campaign outside of Washington.

"You know something?" Kennedy shouted. "You can't remain in the White House for the period of the last six months and understand the anguish and the pain that millions of Americans are feeling with runaway inflation.

"You just can't do it, Mr. Carter. You've gotta come on out and face. . . ." The rest of the sentence was drowned out by applause.

The rally here, on a breezy, overcast day, was set up on 40 hours' notice after Kennedy's surprise victories in the New York and Connecticut primaries. It was the first big outdoor rally of Kennedy's 5-month-old campaign, and it drew the biggest crowd to date.

The big rally here coincided with a similar surge of support registered at the Kennedy headquarters in Washington.

Kennedy staffers there said that, since Tuesday, the campaign office has been flooded with calls from people all over the country volunteering to help in the race against Carter. "That's a sign that the vote on Tuesday was more than just an anit-Carter protest vote," one staff member said yesterday.

Staffers also reported that there had been a big increase in contributions since Tuesday's victories.

Kennedy's travels today took him from Charleston, W.Va., to Pittsburgh to Indianapolis and finally to Kansas City, Kan., where he will campaign Saturday.

He jabbed hard at Carter at every stop on inflation, interest rates and foreign affairs. As has been his practice, he turned just about every question around to those subjects.

In Charleston this morning, he performed a tour de force of evasion when a questioner noted that the White House is saying his campaign will split the Democratic Party.

"Consider where these words of wisdom are coming from," Kennedy said.

"They're the same people who have guided the economy into an 18 percent interest rate and inflation of 18 percent. They're the same people who have bungled the U.N. resolution at the United Nations and . . . failed to provide a comprehensive energy policy. I don't think their judgments on the political scene are any more valid."

In two news conferences and nine local media interviews today, Kennedy was asked just once about family matters. In recent weeks, the proportion of such questions had been much higher.

Kennedy stopped in Charleston this morning to file his entry form for the state's June 3 primary.

He was greeted there by a zestful secretary of state, A. James Manchin, who quoted liberally from John F. Kennedy and who, upon receiving Kennedy's application and filing fee, said, "Ladies and gentlemen, rejoice, the coffers of our great state have just been enriched by $2,000."

Kennedy then flew to Pittsburgh and motored downtown. A Pittsburgh police captain in the entourage seemed stunned when he reached Mellon Square and saw the mob scene there. "That's big," he said. "That's a lot of people. Other policemen said today's event drew more participants than a celebration held in the same spot last January after the Pittsburgh Steelers won the Super Bowl.

In the Kennedy campaign, it is not clear to what degree crowd size translates into political support. As a certified celebrity, Kennedy generally gets a big audience wherever he goes. He was speaking before large and apparently enthusiastic crowds all over Iowa in January, for example, and Carter clobbered him there.

The crowd today seemed receptive to, if not wildly enthusiastic about, Kennedy's call for an immediate wage-price freeze and his suggestion that Carter's White House should be called the "surprise administration" because it has been surprised so often in foreign affairs.

The loudest cheer of the day, though, came in response to Kennedy's jibes, uttered in "I-dare-you" tones at Carter's refusal to campaign.

Two months ago, Kennedy hit Carter's "Rose Garden" campaign hard on the contention that the president was subverting the democratic process by refusing to debate. Now, the theory has changed somewhat: the president's failure to leave the White House prevents him from recognizing the human concerns of the American people, Kennedy says.