A merry go around is not good enough?
Ok...a door then. A heavier door is harder to swing open than a lighter door, because it has a greater moment of inertia. If you get someone to hang at the end of the door, the moment of inertia is even greater.
Or, try traking a heavy book or weight with each hand. Hold them close to your body, and try spinning around. Now spread your arms out (while still holding the weights) and try spinning. You'll notice it's harder to get yourself spinning with your arms spread out. While still spinning with your arms spread out, try bringing them in close to your body...you'll notice that your body will automatically try to spin faster. It's because it has the same energy (due to the spinning), but you're decreasing its moment of inertia by bringing your arms in. Same energy+lower moment of inertia=faster spinning.
Moment of inertia is the same thing as regular inertia (the heavier something is, the harder it is to get moving), except the motion applies to a spinning motion around an axis.