Mechanics
The Mechanics domain tests how you describe and predict motion using kinematics, Newton's laws, conservation of energy, momentum, circular motion, and gravitation. Questions usually combine two ideas-for example, a force problem that must be finished with energy-so identify the principle that makes each step shortest.
Kinematics
For constant acceleration only: v = v₀ + at, Δx = v₀t + ½at², and v² = v₀² + 2aΔx. In two dimensions, treat x and y independently but share the time. Free fall uses a = g ≈ 9.8 m/s² downward; choose a positive direction and keep it.
Forces and Newton's laws
ΣF = ma. Weight is mg, normal force is perpendicular to the surface (N = mg cosθ on a frictionless incline, not mg), and friction satisfies f ≤ μN. Tension pulls along a rope. Newton's third-law pairs act on different objects, so they never cancel in one object's free-body diagram.
Energy and momentum
Work is W = Fd cosθ; kinetic energy ½mv²; gravitational potential energy mgh; spring energy ½kx². Mechanical energy is conserved when only conservative forces do work. Momentum p = mv is conserved in collisions and explosions; impulse J = FΔt = Δp. Kinetic energy is conserved only in elastic collisions.
Circular motion and gravitation
Centripetal acceleration a_c = v²/r points toward the center; it is the net inward force, not an extra force. Gravitational force F = Gm₁m₂/r², and g = GM/r² at distance r from a planet's center.
Worked example
A 2.0 kg block starts from rest and slides 5.0 m down a frictionless 30° incline. Find its speed at the bottom. The vertical drop is h = 5.0 sin30° = 2.5 m. Energy conservation gives mgh = ½mv², so v = √(2gh) = √(2 × 9.8 × 2.5) ≈ 7.0 m/s. The mass cancels; using forces and kinematics gives the same result but takes longer.
Traps that cost marks
- Using x instead of Δx, or mixing up initial and final velocities.
- Writing N = mg on an incline or in an accelerating elevator.
- Giving centripetal force its own arrow outward.
- Forgetting that momentum is a vector and has sign.
- Rounding g to 10 m/s² when the problem specifies 9.8.