Wrap the lump of plasticine around the dowel, about 10cm from the one end.
Hold you had out with your palm facing upwards.
Place the end of the dowel with the plasticine lump into the centre of your hand with the stick facing straight up.
Let go of the dowel with the other hand and try to keep the dowel upright. Try to keep it balanced.
Swap the ends of the dowel around so that the plasticine end is furthest from your hand.
Try to balance the dowel in the palm of your hand.
You can also try this activity with household items that are similarly weighted, objects like a broom.
What's happening?
You should find that the dowel is easy to balance when the lump of plasticine is furthest from your hand. What you are experiencing is rotational inertia.
To understand rotational inertia, it helps understand inertia. Inertia is a "resistance to change of motion". The more inertia an object has, the less it responds to being pushed. For linear motion, moving in a straight line, the measure of an object's inertia is its mass. The more mass in an object, the less it responds to being pushed. A light push sends a ping-pong ball flying, while a light push on a bowling ball has almost no noticeable effect.
Rotational inertia refers to an object that is moving in a circular motion. When the stick begins to topple it will actually move in a circular motion around your hand, which is the axis of rotation. The farther away the mass is located from the axis of rotation (your hand), the greater the rotational inertia and the slower the stick turns. This means the stick is resistant to move and therefore moves slower. Rotational inertia is a measure of an object's resistance to rotation. The more mass the object has, the more inertia and therefore the more resistant to object is to move.
The dowel rotates more slowly when the mass is at the top, allowing you more time to adjust and maintain balance. When the mass is at the bottom, the stick has less rotational inertia and tips more quickly.
Rotational inertia is a resistance to change of rotation. The more rotational inertia an object has, the less it responds to being spun. The outside parts of a spinning object have to move much faster than inside parts near the axis.
The rotational inertia of an object increases the further the mass is from the axis of rotation.
Applications
Imagine at the playground two swings side by side. On one swing is a small child and on the other swing a heavy adult. The heavy weight adult on the playground swing would be much harder to move than the light weight child because the adult weighs more, and therefore has more inertia.
Picture a figure skater spinning (rotating) very quickly. When the skater's legs and arms are tucked close to their body, they spin very fast. This is because their mass is very close to their axis of rotation. When a figure skater changes their position, by extending their arms, their mass is redistributed further from their axis of rotation. This increases their rotational inertia, which results in the skater spinning more slowly. A diver uses the same principle to control the speed of their rotation.
The dowel rotates more slowly when the mass is at the top, allowing you more time to adjust and maintain balance.
When the mass is at the bottom, the stick has less rotational inertia and tips more quickly.