Examples include a light bulb, a screw, a nail, etc.

I intuitively know how these objects behave, but I’m having trouble putting it into words/reasoning about it.

Is it because of the tilt? The diameter difference (this causes the tilt)?

In: 9

It’s the difference in how big around the two ends are. For each rotation of the object the two ends travel a different distance along the ground. Since the bigger end travels further, it curves around the smaller end.

Take a light bulb lying on its side. The bulb itself has, let’s say, twice the diameter as the base. If now the object rotates, every part of it will do the same amount of rotation, or the same angle. When doing this, the bulb will move twice as far as the base at the respective point of contact with the surface. This is just like if you would walk taking twice as big steps with one of the legs, resulting in a curve.

First, let’s start with a cylinder. When a cylinder rolls 360 degrees, it will travel the same distance as it’s circumference (if the cylinder was 1m around, then when it rolled 360 degrees it would travel exactly 1m). It travels in a straight line because both ends of the cylinder have the same circumference, meaning both ends travel the same distance when they rotate.

If we change the circumference of one of the ends of a cylinder to make it smaller, then for every 1 rotation of the object, one side will be traveling a lot less than the other causing it to spin. This is similar to how if one person in a canoe isn’t rowing as fast as the other, the canoe spins.

Diameter difference. The entire item must turn the same number of times no matter the size of the two ends. But the fat end will travel farther in the same number of revolutions.