Laws of Motion and Friction

In JEE, Newton's laws are used as a working framework. The first law identifies equilibrium, the second law gives the equation $\sum \vec F = m\vec a$, and the third law links interactions between bodies. The real skill is deciding the system before writing equations.

A free-body diagram must show only the real forces acting on the chosen body: weight, normal, tension, friction, spring force, or any externally applied force. Do not draw action-reaction pairs on the same body.

Static friction is not automatically equal to $\mu_sN$. It adjusts to whatever value is needed to prevent slipping, up to a maximum of $\mu_sN$. Once slipping begins, kinetic friction takes over with magnitude approximately $\mu_kN$.

Friction opposes relative motion or the tendency of relative motion. In non-inertial frames, if you choose to solve in the accelerating frame, include pseudo force consistently on every mass in that frame.