M.13(1) - MOMENT OF INERTIA OF A DISK AND A RING

A wooden disk and a metal ring with the same diameter (15 cm) and equal mass (605 grams) roll with different accelerations down an inclined plane. One can show that the ring and the disk have the same diameter by superpostion and the same mass by placing them on a balance. Now, if both are rolled along the lecture bench by being given an equal impuse, the metal ring will continue to roll longer than the disk because of its greater moment of inertia. However, when the ring and disk are released simultaneously from the same height on an inclined plane, the wooden disk reaches the bottom first due to its lesser moment of inertia.

Disks, rings, and spheres can be set to roll down the plane showing that all spheres beat disks and all disks beat rings. At the same time, all spheres roll alike as well as all disks and all rings.

M.13(2) - AXIS OF ROTATION

It exemplifies the tendency that a body has to rotate about its axis of greatest moment of inertia. A ring, a chain and a cylinder each hanging on a string are tied in turn to the hook of the rotator spindle. As the rotator runs, with the ring tied to it, the string will be twisted and soon the ring will take up a horizontal position. When the chain is set-up, the final position will be a flattened loop on the horizontal plane. The same happens with the cylinder: initially hanging on the vertical position, as it is rotated, it takes up the horizontal position. This can also exemplify the tendency in nature to reduce the expenditure of energy of any system to a minimum -- the distance between the center of gravity of those objects and the suspension point tends to decrease.

M.13(3) - ROLLING AND SLIDING - ENERGY OF ROTATION

It exemplifies the tendency that a body has to rotate about its axis of greatest moment of inertia. A ring, a chain and a cylinder each hanging on a string are tied in turn to the hook of the rotator spindle. As the rotator runs, with the ring tied to it, the string will be twisted and soon the ring will take up a horizontal position. When the chain is set-up, the final position will be a flattened loop on the horizontal plane. The same happens with the cylinder: initially hanging on the vertical position, as it is rotated, it takes up the horizontal position. This can also exemplify the tendency in nature to reduce the expenditure of energy of any system to a minimum -- the distance between the center of gravity of those objects and the suspension point tends to decrease.

M.13(4) - FALLING BALL AND HINGED STIC

The free end of a falling hinged stick (a narrow board) falls faster than a free-falling ball placed at the other end of the stick, when their center of masses accelerate at an equal rate.

The apparatus is one meter long and consists of two wooden boards mounted one above the other and hinged together at one end. Near the other end of the top board there is a clear plastic cup and at the very tip of the board, a small support for a steel ball. With the apparatus on a flat surface, hold the upper board at about 45°. Set the ball on the support and let the board go.

Surprisingly, the ball will end up in the plastic cup, when the two boards are sitting together. It can also be tried with a plastic ball to show that this works regardless of the ball's mass.

M.13(5) - THE ABERRANT CANDLE FLAME

The apparatus is a wooden platform (40 cm long and 6 cm wide) connected at its center to a variable speed rotator with a clear plastic cylinder (8 cm tall and 5 cm in diameter) at each end. Inside each cylinder, there is a candle. As one lights them up, with the platform still, the flames are vertical. When the platform begins rotation around its central axis, the flames begin to slant inwards -- pointing to each other.

M.13(6) - MOMENT OF INTERIA APPARATUS

This set-up consists of two apparently identical disks, with the same mass but with a different mass distribution: one has a massive center and the other a massive outer ring.

A thread is wound around each axis and extended over a pulley to support a weight. As one lets the weights drop, the disk will spin around their axes: the disk with a massive outer ring has a larger moment of inertia, thus rotating slower than the plastic one.