Mechanics + electromagnetism¶

What you will develop¶

Convert forces, fields and conservation laws into predictive models; move between particle, rigid-body, orbital and field descriptions.

Before you begin¶

Recorded prerequisites:

Study and practice¶

Progress by the work you can do, not by a fixed calendar.

Practice sequence 1¶

Spine: OpenStax University Physics Vol. 1

Reading: Ch. 5-6 Newton's laws and applications

Know: Build free-body models; choose inertial frames; connect constraints/friction/drag to acceleration.

Reconstruct: Derive Newton's second law for coupled bodies and inclined-plane constraints from vector components.

Do: Model a two-actuator robot carriage with friction/saturation; predict acceleration before simulation.

Defend: When is a force model explanatory versus merely a fitted residual?

Gate: Pass: unseen FBD -> equations -> limiting/unit checks -> simulation agreement.

Source: source

Practice sequence 2¶

Spine: OpenStax University Physics Vol. 1

Reading: Ch. 7-9 work/energy, potential energy, momentum/collisions

Know: Switch between force-time and energy/momentum descriptions; identify conserved quantities and dissipation.

Reconstruct: Derive work-energy theorem and impulse-momentum theorem; derive two-body center-of-mass relation.

Do: Compare a regenerative actuator design using force-domain and energy-domain models.

Defend: Which representation makes a given constraint easiest to see?

Gate: Pass: solve one collision/actuation problem by two independent conservation approaches.

Source: source

Practice sequence 3¶

Spine: OpenStax University Physics Vol. 1

Reading: Ch. 10-13 rotation, angular momentum, elasticity, gravitation

Know: Model rigid-body rotation, torque, inertia, angular momentum and basic orbital/gravitational motion.

Reconstruct: Derive rotational kinetic energy, torque-angular acceleration, and circular-orbit speed/period scaling.

Do: Compute spin-gravity profile and structural load scaling for a small rotating-habitat concept.

Defend: What changes when a point-mass model becomes an extended body?

Gate: Pass: derive orbit/rotation scalings and identify at least two ignored structural effects.

Source: source

Practice sequence 4¶

Spine: OpenStax University Physics Vol. 2

Reading: Ch. 5-8 electric fields, Gauss, potential, capacitance

Know: Move between charge, field, potential and stored electric energy; exploit symmetry with Gauss's law.

Reconstruct: Derive field/potential relation and parallel-plate capacitance scaling.

Do: Model an electrostatic sensor/actuator; quantify force/energy vs gap and voltage.

Defend: Why is potential often computationally easier than field?

Gate: Pass: solve one symmetric field problem and one energy/capacitance design problem.

Source: source

Practice sequence 5¶

Spine: OpenStax University Physics Vol. 2

Reading: Ch. 9-14 current, circuits, magnetism, induction, inductance

Know: Model current networks and magnetic forces/fields; understand induction and inductive energy storage.

Reconstruct: Derive RC/RL time constants and Faraday/Lenz sign from flux change.

Do: Build/simulate a solenoid or motor-like magnetic actuator including electrical time constant.

Defend: Where does the mechanical energy come from in an electromagnetic actuator?

Gate: Pass: energy accounting closes across electrical and mechanical domains.

Source: source

Practice sequence 6¶

Spine: OpenStax University Physics Vol. 2

Reading: Ch. 15-16 AC circuits and electromagnetic waves

Know: Reason about impedance, resonance, power and field propagation; connect circuits to waves.

Reconstruct: Derive series RLC resonance and average AC power; derive wave-speed relation conceptually from Maxwell structure.

Do: Design a resonant wireless-power/sensing toy model and quantify detuning sensitivity.

Defend: When does a lumped circuit model stop being valid and a field/wave model become necessary?

Gate: Module defense: unfamiliar electromechanical system -> forces/fields/energy/circuit model + validity limits.

Source: source

Exit gate¶

Closed-book: 150 min closed-book: FBD/conservation/orbit/rotation/electric-field/circuit/induction problems.

Novel problem: Unfamiliar electromechanical device: choose force/energy/field/circuit representation and predict behavior before simulation.

Artifact: Simulate or build an actuator/sensor/orbit subsystem with full energy accounting.

Defend: Defend frame, conserved quantities, approximations, lumped-vs-field model boundary.

Pass criterion: Pass if independent force/energy calculations agree and model validity limits are explicit.

Transfer problems¶

Try these before consulting solutions or asking for the complete answer.

Free body: A magnetic levitation carriage accelerates while cable drag and rolling losses vary with speed. Draw the minimal force model and identify what must be measured.
Conservation: Solve a regenerative braking event by force-time and energy methods; reconcile losses.
Rotation: A habitat spins for 0.8g at its rim. Derive radius/rpm tradeoff and Coriolis scale for a walking occupant.
Orbit: Compare delta-v and energy intuition for raising a circular orbit versus increasing speed locally.
Electrostatics: Design a capacitive gap sensor; derive sensitivity and identify pull-in/nonlinearity risks.
Circuit: Reduce a multi-source resistive network to Thevenin form as seen by a sensor.
Magnetism: Estimate force scaling of a solenoid actuator and identify saturation/thermal limits omitted by ideal theory.
Induction: Predict sign/magnitude trend of induced voltage for changing magnetic flux and validate numerically.
Resonance: Tune an RLC/mechanical analogue and map damping vs peak response.
Model boundary: Give an example where lumped-circuit assumptions fail and field propagation must be modeled.