Mechanics applies mathematics to motion and forces. It combines algebra, calculus, and trigonometry to model real-world physical situations — a required component of the A Level.
Constant acceleration (SUVAT): v = u + at, s = ut + ½at², v² = u² + 2as, s = ½(u+v)t. Displacement-time graph: gradient = velocity. Velocity-time graph: gradient = acceleration, area = displacement. Variable acceleration (calculus): v = ds/dt, a = dv/dt = d²s/dt². s = ∫v dt, v = ∫a dt. Free fall: a = g ≈ 9.8 m/s² (or 10). Projectile motion: horizontal (constant velocity) and vertical (acceleration g) treated independently.
First law: body remains at rest or in uniform motion unless acted on by a resultant force. Second law: F = ma (resultant force = mass × acceleration). Third law: for every action, an equal and opposite reaction. Resolving forces: break into components (horizontal and vertical, or parallel/perpendicular to slope). On inclined plane: component down slope = mg sinθ, normal reaction = mg cosθ. Friction: F ≤ μR (limiting friction = μR). Connected particles: pulleys, tow-ropes — consider each particle separately or the system as a whole.
Work = force × distance in direction of force. KE = ½mv². PE = mgh. Conservation of energy: total energy constant (no external forces). Power = Fv (force × velocity) or work/time. Moments (M4): moment of force = force × perpendicular distance from pivot. Equilibrium: sum of clockwise moments = sum of anticlockwise moments, and resultant force = 0.
Use energy methods (work-energy theorem or conservation of energy) when: (1) you need to relate speed to position without considering time; (2) forces act over a distance; (3) the motion is not in a straight line (e.g., roller coasters, pendulums); (4) questions mention height changes or ask about speed at a point. Use Newton\'s laws (F = ma) when: (1) you need acceleration or time; (2) you need to find forces (tension, normal reaction); (3) the question involves connected particles. Sometimes both approaches work — choose the one that avoids simultaneous equations. For complex problems, you may need both.
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