Mechanics and Gravitation
Core concepts
Newton's three laws underpin everything here: inertia, F = ma as a vector relation, and action–reaction pairs acting on different bodies. Extend to work–energy (work is the line integral of force; conservative forces admit a potential), impulse–momentum (J = Δp), and conservation laws, which are the fastest route through most problems. For rotation, master torque τ = Iα, angular momentum L = Iω, and the parallel-axis theorem I = I_cm + Md². Orbital mechanics: Kepler's three laws, vis-viva v² = GM(2/r − 1/a), and the distinction between escape speed √(2GM/r) and circular-orbit speed √(GM/r).
Traps
Questions love conflating centripetal and centrifugal force, or asking for the normal force at the top of a loop where N = mv²/r − mg can vanish. Friction problems often hide a static-friction maximum μ_s N that must be checked before assuming slipping. In gravitation, remember g = GM/r² falls off outside the body but grows linearly inside a uniform sphere. Watch for the reduced mass in two-body problems and for energy sign conventions (bound orbits have negative total energy).
Worked example
A satellite orbits at radius r with speed v. Doubling r changes circular speed by 1/√2 and orbital period by 2^(3/2) ≈ 2.83, since T² ∝ r³. Rule of thumb: circular speed and period both follow from setting gravitational force equal to mass times centripetal acceleration-derive rather than memorize.