Mechanics
What this domain tests
This mechanics review develops kinematics, Newton's laws, momentum, rigid-body equilibrium, circular motion, oscillations and gravitational ideas. State sign conventions, resolve vectors and justify the choice of force, energy or momentum methods. These are shared foundations rather than a claim about any current regional paper.
Kinematics and projectiles
Use the constant-acceleration equations only when acceleration is uniform. For a projectile, resolve the launch velocity into u cosθ (horizontal, constant) and u sinθ (vertical, changing at g). Time of flight comes from the vertical motion; the range comes from horizontal displacement over that time.
Forces, momentum and equilibrium
- Newton's second law uses the resultant force: F = ma. Weight W = mg acts at the centre of gravity.
- Total momentum p = mv is conserved separately in each direction when the net external impulse on the chosen system is zero; elastic collisions also conserve kinetic energy, inelastic ones do not.
- A body in equilibrium has ΣF = 0 and Σmoments about any point = 0. Take moments about the point with the most unknown forces so those unknowns vanish.
- For circular motion the radial resultant force is mv²/r = mω²r toward the centre. Speed is constant only in uniform circular motion; nonuniform motion also has tangential acceleration.
- SHM is defined by a = −ω²x, with T = 2π/ω; energy shuttles between kinetic and potential.
Worked example
In a uniform-gravity model with no air resistance, a ball leaves level ground at 25 m/s at 40° above the horizontal and lands at the same height. Find its range (g = 9.81 m/s²).
Vertical component: 25 sin40° = 16.07 m/s. Time to the top: 16.07/9.81 = 1.638 s, so total flight = 3.276 s. Horizontal component: 25 cos40° = 19.15 m/s. Range = 19.15 × 3.276 = 62.7 m. Cross-check with R = u² sin2θ/g = (625 × sin80°)/9.81 = 62.7 m. ✓
Traps that cost marks
- Swapping sin and cos: the component next to the angle uses cosine.
- Forgetting that at maximum height the vertical velocity is zero while the horizontal velocity is unchanged.
- Mixing g = 10 with data intended for 9.81, or dropping units mid-calculation.
- Sign errors - fix a positive direction and apply it to displacement, velocity and acceleration consistently.
- Calling circular motion "constant velocity", or omitting the direction of the centripetal force.
- Ignoring the mass of a rod or pulley, or treating a rough surface as smooth when friction is asked for.