I would like to place a periodically rotated (replaced, automatically changed) inspirational quotes
in a side bar. There is a nice plugin for it: rotating posts..
It creates a widget that rotates posts from a specified category, showing automatically one in a time for a specified number of seconds. It works in Twenty Thirteen theme, but doesn't work in Atahualpa. Is there any trick to make it work?

I just installed it and I don't see any widget it adds

I am sorry, it doesn't crate a widget. It uses a shortcode [rotating posts]. I think there might be a better plugin which would create a widget.