After leaving Caltech, Wooldridge moved first to Bell Laboratories, where he worked on the theory of magnetism. In 1946, he and Simon Ramo (his classmate at Caltech) both became director of research for the electronics department of Hughes Aircraft, and his career became coupled with that of Simon Ramo. Together they formed an incredibly successful team for many years, with Wooldridge concentrating on investment and general business aspects while Ramo led research, development and engineering efforts. By 1948, Hughes had created its Aerospace Group to work with the also newly created U.S. Air Force. Ramo and Wooldridge were particularly concerned when Howard Hughes avoided their attempts to discuss the problem. In September 1953 they jointly resigned, and within a week they formed the Ramo-Wooldridge Corporation on September 16, 1953.
In 1958, Ramo-Wooldridge merged with Thompson Products to form TRW, which carried on the success of its predecessor. (In 2002, TRW was bought by Northrop Grumman.) Wooldridge served as president of TRW until he retired in 1962.