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  1. Noether’s Theorem: Symmetry→Conservation Law.

    Symmetries of the action imply conserved quantities per Noether's theorem.

    A path q(t) is shifted by δq = φ but smoothed in transition layers τ wide at t0 and t1, where Δq̇ ≈ φ/τ. Action changes there approximate ΔS ≈ (∂L/∂q̇) Δq̇ τ ≈ −(∂L/∂q̇ φ)(t1) and ≈ +(∂L/∂q̇ φ)(t0).
    Symmetry sets total ΔS = 0, hence (∂L/∂q̇ φ) is conserved from t0 to t1.

    Momentum conservation's derivation from space translation symmetry and energy conservation from time translation symmetry in mechanics and physics is done by it.

    #NoethersTheorem #Physics #TheoreticalPhysics #ClassicalMechanics #AnalyticalMechanics #LagrangianMechanics #Symmetry #ConservationLaws #ActionPrinciple #CalculusOfVariations #Mathematics #STEM #Science #PhysicsEducation #LearnPhysics #QuantumPhysics #FieldTheory #GeneralizedCoordinates #MomentumConservation #EnergyConservation #AngularMomentum #TheoreticalScience #PhysicsNotes #Infographic #ScienceCommunication #EducationalContent #EMNoether #MathPhysics #PhysicsStudents #STEMEducation

  2. It's the time between the Winter Solstice and Christmas, and the forthcoming New Year... the perfect time to put a bowling ball (attached to the ceiling by cable) to one's chin, let it go, hold REAL still, and see what happens next.

    media.cooleysekula.net/w/wtcjW

    #physics #learning #ConservationLaws #NewtonsLaws

  3. Interested in introductory #physics at the #university level? Check out my lecture playlist from when I taught Physics I (PHYS 1303/1307) at Southern Methodist University. The #lectures each focus on a topic and so can be cherry-picked, etc.

    I taught using a flipped classroom model, with peer mentoring and active learning during class.

    media.cooleysekula.net/w/p/2Pp

    #mechanics #NewtonsLaws #Energy #ConservationLaws #Momentum #Motion #Force