UPDATE: beware, Yahoo Pipes has now been shutdown by Yahoo! and the Google Feed API has been deprecated. Check superfeedr.com's API which also does RSS to JSON conversion.
You can use google feed api service
Example:
https://ajax.googleapis.com/ajax/services/feed/load?v=2.0&q=http://phys.org/rss-feed/&num=20
Structure https://ajax.googleapis.com/ajax/services/feed/load?v=2.0&q=RSS_URL_TO_CONVERT&num=
Also if you want better control on RSS conversion use http://pipes.yahoo.com/pipes/ where you can visualize data flow.
EDIT:
As yahoo pipes is no more working, here are the list of alternatives
http://www.makeuseof.com/tag/12-best-yahoo-pipes-alternatives-look/