ZIMSEC · A Level
Mechanical Mathematics
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Form 5 · Lower 6 5 topics
- Kinematics Velocity v = ds/dt; acceleration a = dv/dt = d²s/dt². Conversely, s = ∫v dt and v = ∫a dt (use initial conditions for constants).
- Forces, equilibrium and friction Resolve forces into perpendicular components (usually horizontal and vertical, or parallel and perpendicular to a slope). For equilibrium, the components in each direction sum to zero. Lami's theorem: for three forces in equilibrium, P/sin α = Q/sin β = R/sin γ (angles opposite each force).
- Newton's laws and connected particles Resultant force = ma, applied in the direction of motion.
- Projectiles A particle moving under gravity only (no air resistance), with constant acceleration g downwards.
- Work, energy and power Power = rate of doing work = Fv (W). At maximum speed, the driving force equals the resistance.
Form 6 · Upper 6 3 topicsExam year
- Momentum, impulse and collisions Momentum = mv (N s). Impulse = force × time = change in momentum.
- Moments and centres of mass Moment = force × perpendicular distance. For a rigid body in equilibrium: resultant force zero and total moment about any point zero.
- Circular motion and simple harmonic motion Angular speed ω; v = rω; acceleration towards the centre = v²/r = rω².