Mechanics
Mechanics
This domain covers kinematics, Newton's laws, circular motion, work and energy, momentum, and gravitation. Items often combine a motion graph or diagram with a force analysis, so identify the system and choose a coordinate axis first.
Core rules
- For constant acceleration: v = v₀ + at, Δx = v₀t + ½at², and v² = v₀² + 2aΔx. Use separate horizontal and vertical equations for projectiles; vertical acceleration is g downward and horizontal acceleration is zero when air resistance is neglected.
- Newton's second law, ΣF = ma, is a vector equation. On an incline, weight components are mg sinθ along the slope and mg cosθ perpendicular; static friction satisfies f ≤ μN.
- Work is W = Fd cosθ; the work-energy theorem sets net work equal to ΔK. Mechanical energy is conserved only when nonconservative work is zero.
- Impulse J = FΔt = Δp; momentum is conserved in a system when net external force is zero. Collisions can conserve momentum while losing kinetic energy.
- Uniform circular motion needs centripetal acceleration v²/r toward the center. Gravitation: F = Gm₁m₂/r², and circular satellite orbits obey GM/r = v².
Worked example
A ball rolls off a 1.25 m table horizontally at 6.0 m/s. Vertical motion starts from rest: 1.25 = ½(9.8)t², so t = √(2.50/9.8) ≈ 0.505 s. Horizontal velocity stays 6.0 m/s, so range x = (6.0)(0.505) ≈ 3.0 m. Final vertical speed is gt ≈ 4.9 m/s, giving total speed √(6.0² + 4.9²) ≈ 7.7 m/s.
Traps
- Setting v = 0 at the top of a projectile but forgetting that horizontal v is unchanged.
- Adding centripetal force as an extra outward force; it is the net inward force.
- Assuming kinetic energy is conserved in every collision.
- Mixing mass and weight (mg) in force equations.