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Statics & dynamics · first-year engineering

Engineering Mechanics

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Statics: Forces and Moments

  • L1
    Reading the forces
    newtons, kilograms, pascals, newton-metres
    ★★★★★
    Start
  • L2
    Weight and mass
    W = mg · the kilogram-newton confusion, priced
    ★★★★★
    Start
  • L3
    Resolving on the incline
    sin θ down the slope, cos θ into it
    ★★★★★
    Start
  • L4
    Friction holds
    μₛ before the slide, μₖ during it, tan θ at the tipping point
    ★★★★★
    Start
  • L5
    The moment of a force
    τ = rF sin θ · the arm is half the answer
    ★★★★★
    Start
  • L6
    Levers and pulleys
    mechanical advantage, and what friction takes back
    ★★★★★
    Start
  • L7
    Beam reactions
    the near support carries more — and by how much
    ★★★★★
    Start
  • ★
    The Free-Body Final
    the boss · no calculator · one rig, fully balanced
    ★★★★★
    Start

Dynamics of a Particle

  • L9
    Newton's second law
    F = ma, asked all three ways
    ★★★★★
    Start
  • L10
    Kinematics revisited
    uniform acceleration, now with plant numbers
    ★★★★★
    Start
  • L11
    The no-time equation
    v² = v₀² + 2ad · when the clock is missing
    ★★★★★
    Start
  • L12
    Down the incline
    a = g sin θ, and what friction takes off it
    ★★★★★
    Start
  • L13
    Ropes and tension
    T = m(g + a) · the hoist that reads heavy
    ★★★★★
    Start
  • L14
    Drag and terminal speed
    F = ½CdρAv² · and the speed where drag wins
    ★★★★★
    Start
  • ★
    The Elevator Test
    the boss · no calculator · rope to ramp to verdict
    ★★★★★
    Start

Work, Energy, Momentum

  • L16
    Work done
    W = Fd cos θ · the sideways pull that does nothing
    ★★★★★
    Start
  • L17
    Two energy accounts
    ½mv² for motion, mgh for height
    ★★★★★
    Start
  • L18
    The work–energy theorem
    net work IS the change in kinetic energy
    ★★★★★
    Start
  • L19
    Springs store it
    kx is linear, ½kx² is not — and that gap is the lesson
    ★★★★★
    Start
  • L20
    Power delivered
    the same job, done faster, costs more machine
    ★★★★★
    Start
  • L21
    Momentum and impulse
    p = mv, and the crumple zone that buys time
    ★★★★★
    Start
  • L22
    Collisions
    stick together, bounce apart — momentum survives both
    ★★★★★
    Start
  • ★
    The Runaway Ramp
    the boss · no calculator · energy in, friction out
    ★★★★★
    Start

Rotation and Vibration

  • L24
    Angular kinematics
    ω, α and the rim speed they set
    ★★★★★
    Start
  • L25
    RPM and radians
    the 2π/60 bridge, in both directions
    ★★★★★
    Start
  • L26
    Torque makes it spin
    τ = Iα · and where the mass is sitting
    ★★★★★
    Start
  • L27
    Round the bend
    v²/r and ω²r · the same fact in two dresses
    ★★★★★
    Start
  • L28
    Rotational energy and momentum
    ½Iω² and L = Iω · the analogy, complete
    ★★★★★
    Start
  • L29
    Power through a shaft
    P = τω · and the rpm that must become rad/s
    ★★★★★
    Start
  • L30
    The natural frequency
    √(k/m), and the sag that measures it for you
    ★★★★★
    Start
  • ★
    The Flywheel Final
    the boss · no calculator · rpm to energy to power
    ★★★★★
    Start

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