Game objects clip through another when it moves too fast

I'm trying to make a dice drafting game and decided to get some practice in with Unity and program it (I haven't done too much in 3D). So far what I have is a box for all the dice to be rolled into, a couple of cubes that will be textured for the dice, and a square cup to actually roll the dice. My issue is that while the cup is shaking, the dice will fall out (it is lidded when the dice are loaded) if it moves too fast. I know I probably could just have the cup shake slower, but it seems like it'd be good to know how to prevent this for future reference.