postulate 19.6 Newton's first law

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:112 · p. 734

ground object -- no derivation owed

Rests on

depends_on definition 18.8 Inertial frame of reference ¶
- depends_on definition 18.7 Frame of reference ¶
  - depends_on definition 18.3 Particle ¶
- depends_on definition 18.6 Free particle ¶
  - depends_on definition 18.3 Particle ¶ ↺
depends_on definition 19.5 Linear momentum ¶
- depends_on definition 18.10 Velocity ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶
    - depends_on definition 7.16 Limit ¶
      - depends_on definition 7.2 Absolute value ¶
      - depends_on definition 7.9 Real function ¶
    - depends_on definition 7.9 Real function ¶ ↺
  - depends_on definition 18.9 Position ¶
    - depends_on definition 18.7 Frame of reference ¶ ↺
    - depends_on definition 18.3 Particle ¶ ↺
  - depends_on definition 13.9 Tangent vector to a curve ¶
    - depends_on definition 13.8 Curve ¶
- depends_on definition 19.3 Mass ¶
  - depends_on definition 18.3 Particle ¶ ↺
  - depends_on postulate 19.1 Inertia ¶
    - depends_on definition 18.8 Inertial frame of reference ¶ ↺
    - depends_on definition 18.3 Particle ¶ ↺

Supports

depends_on phenomenon 19.7 Persistence of uniform motion ¶
depends_on postulate 19.19 Newton's first law, rotational case ¶
- depends_on phenomenon 19.21 Equal areas in equal times ¶
- depends_on proposition 20.13 Eastward deflection of a body dropped from rest ¶
  - depends_on remark 20.14 Why the elementary argument gives three halves of this ¶
depends_on postulate 19.8 Newton's second law ¶
- depends_on definition 19.30 Conservative force and potential energy ¶
  - depends_on definition 27.13 Central force ¶
    - depends_on definition 27.14 Central motion ¶
      - depends_on definition 27.16 Areal velocity ¶
  - depends_on definition 19.31 Energy ¶
    - depends_on proposition 27.20 Conservation of energy ¶
    - depends_on theorem 19.32 Conservation of energy ¶
      - depends_on phenomenon 50.6 No material surface ¶
      - depends_on phenomenon 19.33 Mechanical energy is conserved ¶
      - depends_on theorem 21.43 Conservation of energy ¶
  - depends_on proposition 19.71 The Newtonian closed system is a Lagrangian system ¶
- depends_on definition 19.34 Work ¶
  - depends_on definition 19.35 Power ¶
  - depends_on proposition 19.36 Work of a torque ¶
    - depends_on corollary 19.37 Rotational power ¶
  - depends_on theorem 19.38 Work–energy theorem ¶
- depends_on phenomenon 49.16 Pulsars: clocks at nuclear density ¶
- depends_on phenomenon 42.1 Universality of free fall ¶
  - depends_on phenomenon 53.5 Universality of free fall, as measured ¶
    - tests experiment The Eötvös lineage and MICROSCOPE ¶
      - cites (evidence) derived bib Verification of the equivalence of inertial and gravitational mass ¶
      - cites (evidence) derived bib Verification of the equivalence of inertial and gravitational mass ¶ ↺
      - cites (method) derived bib Beiträge zum Gesetze der Proportionalität von Trägheit und Gravität ¶
      - cites (evidence) derived bib Beiträge zum Gesetze der Proportionalität von Trägheit und Gravität ¶ ↺
      - cites (evidence) derived bib Beiträge zum Gesetze der Proportionalität von Trägheit und Gravität ¶ ↺
      - cites (evidence) derived bib 3 The equivalence of inertial and passive gravitational mass ¶
      - cites (evidence) derived bib 3 The equivalence of inertial and passive gravitational mass ¶ ↺
      - cites (method) derived bib 4 Test of the Equivalence Principle Using a Rotating Torsion Balance ¶
      - cites (evidence) derived bib 4 Test of the Equivalence Principle Using a Rotating Torsion Balance ¶ ↺
      - cites (evidence) derived bib 4 Test of the Equivalence Principle Using a Rotating Torsion Balance ¶ ↺
      - cites (method) derived bib 23 MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle ¶
      - cites (evidence) derived bib 23 MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle ¶ ↺
      - … 4 more
  - depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶
    - tests experiment Lunar laser ranging and Gravity Probe B ¶
      - cites (method) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶
      - cites (evidence) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶ ↺
      - cites (evidence) derived bib 22 Gravity Probe B: Final Results of a Space Experiment to Test General Relativity ¶ ↺
      - cites (history) derived bib Über den Einfluß der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie ¶
      - cites (method) derived bib 18 APOLLO: millimeter lunar laser ranging ¶
      - cites (history) derived bib 5 Equivalence Principle for Massive Bodies. II. Theory ¶
      - cites (history) derived bib 5 Equivalence Principle for Massive Bodies. II. Theory ¶ ↺
      - cites (history) derived bib Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie ¶
      - cites (method) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶
      - cites (evidence) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶ ↺
      - cites (evidence) derived bib 26 Progress in Lunar Laser Ranging Tests of Relativistic Gravity ¶ ↺
- depends_on phenomenon 19.10 Force, mass and acceleration ¶
- depends_on postulate 19.22 Newton's second law, rotational case ¶
  - depends_on theorem 29.25 Euler's equations ¶
    - depends_on phenomenon 29.46 A fast spinning top does not fall ¶
      - depends_on phenomenon 29.49 Precession of the equinoxes ¶
    - depends_on phenomenon 29.31 The intermediate-axis instability ¶
      - depends_on remark 29.32 What the linearization is entitled to conclude ¶
    - depends_on proposition 29.26 The two integrals of torque-free motion ¶
      - depends_on proposition 29.33 Dissipation drives a free body to its largest moment ¶
      - depends_on proposition 29.43 The three integrable heavy tops ¶
      - depends_on remark 29.27 Euler's equations as a Lie–Poisson system ¶
      - depends_on remark 29.30 Polhode and herpolhode ¶
      - depends_on remark 24.42 The intermediate axis ¶
      - depends_on theorem 29.29 Poinsot's construction ¶
    - depends_on proposition 29.28 Free rotation of a symmetric body ¶
      - depends_on phenomenon 29.34 Free nutation of the Earth ¶
    - depends_on proposition 24.41 The free rigid body is a Lie–Poisson system ¶
      - depends_on remark 24.48 Reduction is what physicists do without saying so ¶
      - depends_on remark 24.42 The intermediate axis ¶ ↺
- depends_on postulate 19.48 Newton's third law ¶
  - depends_on phenomenon 19.50 Recoil and the conservation of momentum ¶
  - depends_on postulate 19.49 Net internal force ¶
    - depends_on phenomenon 19.54 The centre of mass ignores internal forces ¶
  - depends_on postulate 19.61 Newton's third law, strong form ¶
    - depends_on theorem 19.63 The spin obeys the same law about the centre of mass ¶
      - depends_on phenomenon 19.65 Spin is conserved when no external torque acts ¶
      - depends_on theorem 19.68 Conservation of angular momentum ¶
    - depends_on theorem 19.62 Rotational second law for a system ¶
      - depends_on theorem 19.68 Conservation of angular momentum ¶ ↺
  - depends_on theorem 27.30 Reduction of the two-body problem ¶
    - depends_on phenomenon 27.32 Kepler's first law: bound orbits are closed ellipses ¶
    - depends_on phenomenon 27.35 Kepler's third law ¶
      - depends_on phenomenon 50.5 Black-hole masses from gravitational waves ¶
      - depends_on phenomenon 50.1 Dark companions too massive to be neutron stars ¶
      - depends_on phenomenon 50.2 Four million solar masses inside the orbit of a single star ¶
    - depends_on phenomenon 50.1 Dark companions too massive to be neutron stars ¶ ↺
    - depends_on phenomenon 50.2 Four million solar masses inside the orbit of a single star ¶ ↺
  - depends_on theorem 19.52 The centre of mass moves as a particle ¶
    - depends_on theorem 19.67 Conservation of linear momentum ¶
      - depends_on theorem 19.69 Uniform motion of the centre of mass ¶
- depends_on theorem 20.2 Parabolic trajectory ¶
  - depends_on corollary 20.3 Range, apex, time of flight ¶
    - depends_on example 20.4 ex:projectile-everyday ¶
    - depends_on phenomenon 20.6 Air drag ¶
    - depends_on proposition 20.9 Linear resistance: exact motion, and the lost range ¶
      - depends_on remark 20.11 What has no closed form, and what to do about it ¶
  - depends_on phenomenon 20.6 Air drag ¶ ↺
  - depends_on remark 20.5 rem:projectile-idealisation ¶
- depends_on theorem 29.51 Equation of motion in a rotating frame ¶
  - depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶ ↺
depends_on proposition 19.20 For one particle the rotational first law is not independent ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Inertial frame of reference	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:115
`depends_on`	→	Linear momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:115
`depends_on`	←	Persistence of uniform motion	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:129
`depends_on`	←	Newton's first law, rotational case	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:494
`depends_on`	←	Newton's second law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:161
`depends_on`	←	For one particle the rotational first law is not independent	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:504