A ball on a spinning turntable won't fly off as you might expect. In fact the ball will have it's own little orbit that is exactly 2/7th the angular speed of the table. Here's why.
Here's a paper with the calculations: http://m2.askthephysicist.com/Weltner.pdf Note that equations 18 and 19 should have R² terms. That threw me off for longer than I care to admit!
Pavel Dubov Jeremy Cole Brendan Williams Alan Wilderland Frank Hereford Lukas Biewald Marshall Fitzpatrick Heather Liu Grant Hay John Zelinka Paul Warelis Matthew Cocke Alnitak Damien Szerszinski Lizzy and Jack Nathan Blubaugh