Summary

This chapter developed WBCHSE Unit 3's account of the laws of motion in the following order. Newton's first law defines inertia and identifies inertial frames. Newton's second law, $F = dp/dt$ (reducing to $F = ma$ for constant mass), connects force quantitatively to momentum. Impulse, $J = F\,\Delta t = \Delta p$, describes the overall effect of a large, brief (impulsive) force, and explains why lengthening contact time -- in a cricketer's catch, a bent-knee landing, a car's crumple zone or airbag -- reduces the peak force for a given change of momentum. Newton's third law pairs every action with an equal, opposite reaction acting on a different body, explaining walking, swimming, recoil and rocket propulsion. Combining the second and third laws over an isolated system gives the law of conservation of linear momentum, the basis of recoil, rocket propulsion, collisions and explosions. Free body diagrams isolate one body and its external forces to make any such problem tractable, and the equilibrium of concurrent forces -- vector sum zero, or Lami's theorem for three forces -- extends this to bodies held by several forces at once. Friction was treated in two stages: static friction (self-adjusting, up to $f_{s(\text{max})} = \mu_s N$) and kinetic friction ($f_k = \mu_k N$), followed by the angle of friction and the angle of repose (shown to be numerically equal, both equal to $\tan^{-1}\mu_s$), and rolling friction (much weaker than sliding friction, because it arises from contact-patch deformation rather than gross sliding). Finally, uniform circular motion requires a real, inward-directed centripetal force, $F_c = mv^2/r = m\omega^2 r$, supplied in practice by friction (a level road), by a component of the normal reaction (a banked road, or a leaning cyclist), or by string tension -- worked through for a cyclist, a level road, and a banked road, wi …