When you flip it, hit it with your thumb's fingernail. Think of how you do a coin toss-- just be sure to strike it hard! If there's a distinctive ringing sound, then it's mostly copper. The zinc cores make a much different sound: more of a thud. Go find a penny minted pre-1982 and compare to a new one; you'll hear the difference!
*Edit/Disclaimer: I know that you can tell by the date, but this is way cooler.