Question:

A uniform ladder of mass $m$ and length $l$ leans at an angle $\theta$ against a frictionless wall, Fig. 9–70. If the coefficient of static friction between the ladder and the ground is $\mu_s$, determine a formula for the minimum angle at which the ladder will not slip.

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

$\theta = \tan^{-1} \left( \dfrac{1}{2 \mu_s} \right)$