Understanding how rolling without slipping works can be tricky. It involves figuring out how linear speed and turning speed relate to each other. Here are some of the main challenges:

1. Different Surfaces: The texture of the surface or how steep a hill is can change how something rolls. This can be hard to predict.

2. Complicated Math: To understand the movement, you need to mix two types of speed: how fast something is going straight ($v$) and how fast it is spinning ($\omega$). This can get confusing.

3. Real-life Factors: Things like friction (the force that slows down movement) and what the rolling object is made of can make it harder to use simple theories.

To tackle these problems, it's important to set up experiments in a consistent way. This means creating controlled situations and measuring things accurately. Doing this helps us better understand the important relationship between rolling speed and turning speed:

$v = r\omega$

Here, $r$ stands for the radius, or how big the object is.

Trying out simulations can also help connect what we learn in theory with real life.