Mechanics
Mechanics: what is tested
The Mechanics domain tests kinematics in one and two dimensions, Newton's three laws, work and energy, linear momentum, circular and rotational motion, and gravitation. Questions often combine two ideas-for example, energy conservation followed by a projectile calculation-so identify the principle that avoids unknown forces.
Core rules
- For constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as. These fail when acceleration changes.
- Newton's second law is vector: ΣF = ma. Resolve along and perpendicular to motion; on an incline, the normal force is mg cosθ, not mg.
- Work done by a constant force is W = Fs cosθ; net work equals ΔK. Gravitational potential energy near Earth is mgh; elastic energy is ½kx².
- Momentum p = mv is conserved when net external force is zero. Collisions may conserve momentum but not kinetic energy.
- Circular motion needs a centripetal resultant F = mv²/r = mω²r, directed to the centre. It is not a new force.
- Torque τ = rF sinθ; rotational inertia and angular momentum L = Iω are the rotational analogues of mass and momentum.
- Newton's gravitation F = GMm/r² gives g = GM/r² and orbital speed v = √(GM/r) for a circular orbit.
Worked example
A 2.0 kg block slides from rest 3.0 m down a frictionless 30° incline. Find its speed at the bottom. The vertical drop is h = 3.0 sin30° = 1.5 m. Energy conservation gives ½mv² = mgh, so v = √(2gh) = √(2 × 9.8 × 1.5) ≈ 5.4 m/s. The mass cancels; using acceleration a = g sinθ with v² = 2as gives the same result.
Traps that cost marks
Choose a positive direction and keep it. Do not call mg the normal force on a slope. Static friction has a maximum μN but takes only the value needed to prevent slipping. In circular motion, do not add an outward centrifugal force to a free-body diagram. For momentum, check external impulses such as friction or an exploding spring. For orbits, the radius is measured from the centre of the planet, not its surface.