Thornton Bradshaw, presiding over his first annual meeting as chairman of RCA Corp., spent much of nearly four hours today fielding angry questions from shareholders whose mood wasn't helped by the sharply reduced quarterly dividend that they had just received in the mail.

In his opening remarks, Bradshaw promised better days ahead, but he warned that although "1982 will be a far better year for RCA than 1981, we will still fall short of our true potential."

The quarterly dividend was slashed to 22 1/2 cents a share from 45 cents after the company's disastrous 1981 results, when annual earnings dropped to $54 million from $315.3 million in 1980 on static sales of $8 billion. For the first quarter of this year, the company reported earnings of $60.5 million, up from $42 million in 1981.

Bradshaw said that RCA's woes were a result of the company getting "away from its roots--roots that are intertwined with the history of the electronic industry." RCA's future is in electronics, entertainment and communications, Bradshaw said.

Grant Tinker, the man chosen by Bradshaw as chairman of NBC to bolster the network's fortunes, told the shareholders, "I look at next fall as the beginning of a turnaround for NBC."

Referring to efforts to sell off some of the diverse business acquired by his predecessors, Bradshaw said the search continues for a buyer for Hertz Corp. CIT Financial Corp., another major acquisition, has been profitable and will remain in the RCA fold, he said.

Commenting on rumors that the company is a takeover target whose parts are worth more than RCA's current market value, Bradshaw said management would resist "to the utmost" any "attempt at dismembering this corporation."

The company greeted the recent disclosure that Bendix Corp. had acquired 5.5 million shares of RCA with a strong statement because "we were determined to maintain the independence of RCA," the 64-year-old chairman said.

At the the meeting, held in a spacious NBC studio at Rockefeller Center, the critics included a number of retired RCA employes and other pensioners who rely on dividend income and who are concerned about RCA's future.

Bradshaw, who for the most part listened and made only terse comments, reacted with unusual vehemence when a shareholder said that, because Bradshaw had been a board member since 1972, he shares the blame for the company's current financial reverses.

"The direction of the company was set 12 years ago on the premise that the electronics business had matured," replied Bradshaw, who left the presidency of Atlantic Richfield Co. last year to head RCA. Once the diversification was under way, "You could not turn back the clock because, after all, earnings were increasing," he said.

After Bradshaw introduced his board of directors--which has been trimmed from 15 to 8 members with Bradshaw the only RCA executive on it--there was sharp criticism of the directors' modest holdings of company shares. Of the eight, Bradshaw owns 6,100 shares, but the others have 500 or fewer, with three owning 100 shares. One shareholder was applauded when he asked, "Why don't the directors want to participate in the company's future?"

Bradshaw said the person chosen to fill the open presidency slot will join him on the board. He maintained that companies benefit by having a majority of the board members from outside the organization.

However, stockholders noted that a number of outside directors have close ties to RCA. They pointed out that board member Donald B. Smiley, for example, has a $150,000-a-year consulting contract with RCA and was instrumental last year in the decision to name fellow board member Bradshaw as chairman. Another shareholder commented that director Peter G. Peterson is chairman of Lehman Brothers Kuhn Loeb, which handles about one-third of RCA's investment banking business.