Mechanics spans multiple IAL units: linear motion and forces in Unit 1, energy and momentum in Unit 2, and circular motion and SHM in Unit 4 — a core thread throughout the course.
Kinematics: suvat equations (constant acceleration). v = u + at, s = ut + ½at², v² = u² + 2as. Displacement-time: gradient = velocity. Velocity-time: gradient = acceleration, area = displacement. Variable acceleration: v = ds/dt, a = dv/dt. Newton\'s first law: no resultant force → constant velocity. Second: F = ma (or F = dp/dt). Third: equal and opposite forces on different bodies. Free-body diagrams for resolving forces. Projectiles: horizontal (constant velocity) and vertical (acceleration g) components treated independently. Time of flight, range, maximum height.
Work W = Fs cosθ. KE = ½mv². GPE = mgh. Power P = Fv. Efficiency = useful output / total input. Conservation of energy. Momentum p = mv. Conservation in collisions. Elastic collisions: KE conserved. Inelastic: KE not conserved (some to heat/sound). Impulse = FΔt = Δp. Circular motion: centripetal acceleration a = v²/r = ω²r. Centripetal force F = mv²/r. Angular velocity ω = 2πf = 2π/T. SHM: a = −ω²x. Displacement x = Acos(ωt) or Asin(ωt). v_max = Aω at equilibrium. Examples: mass-spring (T = 2π√(m/k)), pendulum (T = 2π√(l/g)).
In all collisions where no external forces act, total momentum is conserved (p_before = p_after). The difference is kinetic energy: in an elastic collision, total KE is also conserved — the objects bounce off with no energy lost to heat, sound, or deformation. Examples: collisions between gas molecules, some billiard ball collisions. In an inelastic collision, KE is not conserved — some is converted to heat, sound, or deformation. A perfectly inelastic collision is when the objects stick together (maximum KE loss). Most real-world collisions are inelastic. To check: calculate total KE before and after. If they\'re equal → elastic. If KE after < KE before → inelastic.
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