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Mechanics - Coggle Diagram

- - - - Newton's First Law
        
        If no resultant force, object stays at rest or moves at constant velocity
      - Newton's Second Law: F = ma
        
        Resultant force = mass × acceleration
      - Newton's Third Law
        
        Equal and opposite forces on different bodies
    - - Weight: W = mg
      - Newton's Second Law: Fnet = ma
    - - Forgetting that F = ma uses resultant force, not individual forces
      - Drawing incomplete Free Body Diagrams (missing normal reaction, friction, or tension)
  - - - Problems with motion in one dimension (horizontal and vertical)
      - Connected particles (strings over pulleys)
        
        Inextensible string → same acceleration for both particles
      - Motion on an inclined plane
    - - On an incline (no friction): mg sinθ = ma (down the plane)
      - On an incline (with friction): mg sinθ - F = ma
    - - Pulley problems: assuming tension equals weight (T ≠ mg unless at rest or constant velocity)
      - Incline: resolving mg incorrectly (mg sinθ is parallel to plane, mg cosθ is perpendicular)
  - - - Vectors in 2D (component form: xi + yj)
      - Magnitude of a vector (|v| = √(x² + y²))
      - Unit vectors (i and j)
    - - Fx = F cosθ, Fy = F sinθ
      - |v| = √(x² + y²)
    - - Putting sin/cos on the wrong component (check angle with horizontal vs vertical)
  - - - Non-constant acceleration
      - Using differentiation to find velocity and acceleration from displacement
      - Using integration to find velocity and displacement from acceleration
    - - v = ds/dt
      - a = dv/dt = d²s/dt²
      - v = ∫a dt
      - s = ∫v dt
    - - Using SUVAT equations for variable acceleration problems
      - Finding displacement: forgetting to use initial conditions to find the constant of integration
  - - - Friction: force opposing motion or impending motion
      - Coefficient of friction (μ)
      - Normal reaction (R or N): perpendicular contact force
      - Limiting equilibrium: F= μR
      - Rough horizontal surfaces
      - Rough inclined planes
    - - F ≤ μR (static friction, limiting equilibrium)
      - F = μR (kinetic friction, when moving)
    - - Forgetting that friction depends on the normal reaction, not the weight directly
  - - - Work done by a constant force
      - Kinetic Energy (KE)
      - Gravitational Potential Energy (GPE)
      - Conservation of Energy
      - Work-Energy Principle
      - Power: rate of doing work
    - - Work done (W) = Fs (force in direction of displacement)
      - Work done against gravity = mgh
      - Kinetic Energy (KE) = ½mv²
      - Gravitational PE = mgh
      - Conservation of Energy: ½mu² + mgh₁ = ½mv² + mgh₂ + (Work against friction)
      - Work-Energy: ½mv² - ½mu² = total work done by all forces
      - Power (P) = Work / time = Fv
    - - Work done: using distance travelled for constant forces instead of displacement
      - Work done sign: force opposed to motion → negative work
      - Power: using P = Fv but v must be in direction of F (not speed if angle)
  - - - Displacement (s): distance in a given direction from a starting point
      - Velocity (v, u): speed in a given direction (displacement over time)
      - Acceleration (a): rate of change of velocity
      - Scalar vs Vector quantities
        
        Scalars: magnitude only (e.g., distance, speed, mass, time)
        
        Vectors: magnitude and direction (e.g., displacement, velocity, acceleration, force)
      - Displacement-time graphs
        
        Gradient = velocity
      - Velocity-time graphs
        
        Gradient = acceleration
        
        Area under graph = displacement
    - - v = ds/dt (velocity as derivative of displacement)
      - a = dv/dt (acceleration as derivative of velocity)
      - v = ∫a dt (velocity as integral of acceleration)
      - s = ∫v dt (displacement as integral of velocity)
  - - - Equilibrium: resultant force = 0 → object at rest or moving at constant velocity
      - Conditions for equilibrium: ΣFx = 0 and ΣFy = 0
      - Resultant force: vector sum of all forces acting on a body
    - - Equilibrium: ΣFx = 0, ΣFy = 0[reference:36]
      - Resultant: R = √(ΣFx² + ΣFy²)
  - - - Linear momentum (p = mv)
      - Principle of Conservation of Linear Momentum
        
        Total momentum before = Total momentum after (closed system, no external forces)
      - Impulse = change in momentum = Ft
    - - p = mv
      - m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (conservation of momentum)
      - Impulse = mv - mu = Ft
  - - - v = u + at
      - s = ½(u + v)t
      - s = ut + ½at²
      - s = vt - ½at²
      - v² = u² + 2as