Mechanics
Statics, kinetics and dynamics — forces, moments, motion, momentum, stress and gyroscopics.
Statics & dynamics — summary notes
- Statics: bodies in equilibrium — forces and moments balance, nothing accelerates. A moment is a force's turning effect about a pivot.
- Dynamics: bodies in motion — Newton's laws link force, mass and acceleration; work, energy and power describe how forces act over distance and time.
- Momentum is conserved in collisions — relevant to impact loads and gyroscopic behaviour in rotating components (gyros, turbine rotors).
- Friction opposes relative motion; the coefficient of friction (μ) depends on the surface pair, not the contact area.
- Moment
- M = F × d
- Weight
- W = mg
- Newton's second law
- F = ma
- Equations of motion
- v = u + at, s = ut + ½at², v² = u² + 2as
- Work
- W = F × s
- Power
- P = W/t = Fv
- Kinetic energy
- KE = ½mv²
- Potential energy
- PE = mgh
- Momentum
- p = mv
- Conservation of momentum
- m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- Friction force
- F = μN
A lever is pivoted so a 100 N force acts 3 m from the pivot on one side, and a 300 N force acts 1 m from the pivot on the other. Is the lever balanced?
M₁ = 100 × 3 = 300 N·m. M₂ = 300 × 1 = 300 N·m. Since M₁ = M₂, the lever is in equilibrium.
A ground tug accelerates a towbarless aircraft from rest to 5 m/s in 4 seconds. Find the acceleration and distance covered.
a = (v − u)/t = (5 − 0)/4 = 1.25 m/s². s = ut + ½at² = 0 + 0.5 × 1.25 × 4² = 10 m.
Projectile motion
Momentum & collisions
Energy conversion (KE ⇄ PE)
Hooke's law
Simple harmonic motion — the pendulum
Vibration & resonance — standing waves
Statics & dynamics concept map
Statics & Dynamics
Mechanics quiz
Mechanics
1. A 200 N force acts 0.5 m from a pivot. The moment is:
2. Two equal, opposite, parallel forces not in line form a:
3. An object in equilibrium has resultant force and moment both equal to:
4. Work done lifting 50 kg through 2 m (g = 9.81) is about:
5. Newton's second law is F =
6. A 10 kg mass accelerating at 2 m/s² needs a force of:
7. Momentum equals mass multiplied by:
8. The SI unit of momentum is:
9. Newton's third law: every action has an equal and opposite:
10. Kinetic energy is given by:
11. Gravitational potential energy is given by:
12. A 2 kg mass moving at 3 m/s has kinetic energy of:
13. The SI unit of power is the:
14. A machine doing 1000 J of work in 5 s has a power of:
15. Velocity is a ___ quantity.