Columbia, the new city 30 miles north of downtown Washington in Howard County, Md., is one of the most carefully planned communities in the United States. For young people, it has swimming pools, skating rinks, recreation centers, playing fields and bicycle paths galore - everything planners could imagine a teen-ager wanting.

So when Roger Karsk, a Columbia resident working towards his doctoral degree, heard about a "teen-age problem" in Columbia, he decided it was worth studying.

His results did not surprise Columbians: Despite the physical planning and the facilities in the town billed as "The Next America," teenagers are growing up like other teen-agers in other suburban communities, with many of the same problems.

"For teens interested in athletic and other structured programs," Karsk has written in a new book, "Columbia was an enormously rich place." But little attention was given to easing teen-age race relations in the integrated community or finding informal settings for teens to congregate in addition to the teen centers, which turned out to be unpopular.

In Columbia, Karsk found the same distribution of young people as in most places: the highly motivated and the aimless, the sexually active and the inactive, the pot smokers, the straights, the "joks," the "freaks" and the intellectuals.

Most preferred Columbia to their former communities, giving such reasons as "openness," "more friends," "safer" and "more to do." (See TEENS, B8, Col. 1) (TEENS, From B1)

As one teen-ager put it recently in an interview with The Washington Post: "It's a suburd, but it's not, because I can walk anywhere. I can catch a bus anywhere, but it's not a city. We have an open space behind our house where it's nice to sit and breathe without being surrounded by a lot of crackboxes."

"The larger issue never directly faced," Karsk wrote in "Teenagers in the Next America," "was an overall philosophy about teen-agers in this new community. What would their needs be? What would be the ideal settings to meet these needs?"

The first residents of Columbia arrived in 1967 and by 1968 Columbia's fathers were complaining about the youths who congregated in parking lots, use of drugs, and vandalism of new buildings.

From 1971 to 1974, Karsk probed the teen-aged world, surveying teens and parents. The most explicit insights he drew were from a year's worth of daily logs by eight teenagers reprenting a cross section of the community.

A drive through the town of 45,000 located halfway between Washington and Baltimore immediately suggests that physical design has partially dictated teen habits. There are no "street corners," the popular gathering places of teens in the 1950s and 1960s - and there is no conventional downtown.

Many teen-agers flockers to Columbia's enclosed mall but found that few restaurants catered to them and merchants imposed rules on them designed to discourage them from hanging around, Karsk found.

While Karsk conducted his study, use of marijuana and alcohol increased, with alcohol becoming more widespread. In Howard County, 70 per cent of the teens had tried alcohol and 50 per cent continued to use it, while 40 per cent experimented with marijuana and 28 per cent kept using it. "Both the community and the police were much more vigorous in enforcing the marijuana laws than the alcohol laws," Karsk said.

Popularity of acid, "uppers" and "downers" decreased during his study, and he heard of no interest in heroin or other hard drugs.

Seven of Karsk's eight logkeepers recorded their sexual habits. Four of them said they had had intercourse at 14 or younger. Five said that although they were informed about birth control methods they did not use contraceptives when experimenting with sex for the first time and many others brazenly declined to use contraceptives at all. In interviews with medical clinics, Karsk pinpointed a minimum of 10 to 13 teen-age abortions each month.

"What I saw happening . . . was both healthy and a bit frightening," he wrote. "Sexual intercourse was not running rampant, but generally associated with meaningful relationship. Abortions added an alternative to pregnancies."

A survey of adults in 1,000 Columbia households showed that 54 per cent had more friends of other races than they had had in other communities and 64 per cent believed race relations were better in Columbia than elsewhere.

"There existed an assumption about Columbia by the adult residents that school age children and teen-agers would have less racial prejudice than their parents because of more interaction with each other within neighborhoods and school. "In fact, the opposite may be true, especially among teen-agers," Karsk wrote.

Name-calling, distrust and rumours fomented racial friction and fights in the schools. Lower income blacks and middle-class white often kept to themselves, although middle-class blacks associated with both groups.

White students seemed "to be more willing" to associate with blacks of their economic status, but some white students exhibit "high levels of prejudice against blacks in general," he said.

"Columbia may be a model city, yet its residents still brought their stereotypes with them," Karsk wrote.