The coefficient of static friction, which we can call $\mu_s$, is an important idea to understand how different materials stick to each other. It changes a lot depending on the materials involved, especially in 2D systems. Here are some key things I’ve noticed that affect static friction:

1. Material Type: Different materials have very different levels of friction. For example, rubber gripping concrete has a high $\mu_s$ (about 0.6 to 0.9). On the other hand, steel on ice has a low $\mu_s$ (around 0.1 to 0.2). This means that rubber can hold onto concrete much better than steel can hold onto ice.

2. Surface Texture: The roughness of the surface matters too. Rougher materials tend to stick better because their surfaces can grip onto each other. Smooth surfaces often lead to less friction, making it easier for things to slide.

3. Environmental Conditions: How wet or hot it is can change the friction levels. For example, if a surface is wet, the $\mu_s$ usually goes down. This makes it easier for objects to slide around.

4. Normal Force: The weight of an object affects how much force we need to move it. We can think about this as $F_s \leq \mu_s N$, where $F_s$ is the static friction force and $N$ is the normal force (which is basically the weight pushing down).

In summary, knowing about these factors is really important for understanding how things balance and stay still in 2D systems!