May I ask is there any relationship between the angle of the incline plane and the coefficient of dynamic friction? Because as I know, the coefficient of dynamic friction is only related to the material of the surface. But after I searched up some website, it shows that if the angle of the incline plane is bigger, the coefficient will also get bigger with the formula of μ=tan(a).
Thanks in advance
The coefficient of friction depends only on the material properties of the two surfaces in contact, the angle of the contact patch is irrelevant. If you peruse a coefficient of friction table to find a particular value, you will find that the only thing you need to know is what pair of materials are in contact.
It's possible you misunderstood the problem you referenced - it may have been asking you to find the minimum possible coefficient of friction needed to prevent slipping at different angles. As the angle of the incline gets steeper, you need more friction to prevent the block from sliding. You could solve for the coefficient of friction required, and find that it does depend on the angle. But that doesn't imply that when given a particular block and ramp that changing the angle changes the coefficient of friction.
The relationship between the incline angle $\theta$ and the coefficient of static (not dynamic) friction, $\mu_s$ when motion is impending is
$$\mu_{s}=\tan \theta$$
Once sliding, the coefficient of dynamic (kinetic) friction, $\mu_k$, is generally considered independent of $\theta$.
Hope this helps.
