Imagine a round turn table or one of those spinning tables at Las Vegas that they throw dice into. Now imagine this table has a groove or channel, I will call it a slot, deep enough to hold a marble. The slot runs in a straight line starting half way out from the center of the table to the edge circumference allowing the marble to roll away leaving the table, but first the marble is held in place in that slot while the table rotates at an edge circumference velocity of 1 meter a second. I press a button and the marble is released.

Is there a formula or method to figure out what direction the marble will end up leaving the table? Will it leave the table before 90 degrees of rotation or will it take 270 degrees? The velocity of the rotating table and the mass of the marble can vary.

Below is a drawing I made and some relevant information. Thanks.

M-long.jpg
To do this problem with the approach I took, you need H.S. algebra and physics, college pre-algebra (including trigonometry), college calculus (for derivatives and vectors- I didn't use integrals), ordinary differential equations of the second order (i.e., two constants to be resolved using boundary conditions), and college Freshman physics.

You can learn all about these college subjects from Academic Earth, the MIT online website (where you can take the MIT famous 1999 physics class). For the H.S. math subjects, there are a number of online presentation classes that should prove invaluable presenting things in a logical order.