postulate 19.8 Newton's second law

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:158 · p. 735

ground object -- no derivation owed

Rests on

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 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 18.7 Frame of reference ¶ ↺
      - depends_on definition 18.6 Free particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
depends_on postulate 19.6 Newton's first law ¶
- depends_on definition 18.8 Inertial frame of reference ¶ ↺
- depends_on definition 19.5 Linear momentum ¶ ↺

Supports

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 29.36 Three first integrals ¶
      - depends_on theorem 27.10 Lagrange–Dirichlet ¶
- 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 proposition 29.50 The principal nutation ¶
  - 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 29.45 What integrability buys, and where it stops ¶
      - depends_on remark 29.44 The Kovalevskaya integral ¶
    - 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 remark 29.32 What the linearization is entitled to conclude ¶ ↺
      - depends_on remark 29.30 Polhode and herpolhode ¶ ↺
  - 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 example A.573 The abelian case, and eliminating a cyclic coordinate ¶
    - 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 ¶ ↺

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`	→	Linear momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:161
`depends_on`	→	Newton's first law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:161
`depends_on`	←	Conservative force and potential energy	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:831
`depends_on`	←	Work	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1002
`depends_on`	←	Pulsars: clocks at nuclear density	declared	parts/05-general-relativity-cosmology/08-compact-stars.tex:1049
`depends_on`	←	Universality of free fall	declared	parts/05-general-relativity-cosmology/01-equivalence-classical-tests.tex:168
`depends_on`	←	Force, mass and acceleration	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:219
`depends_on`	←	Newton's second law, rotational case	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:590
`depends_on`	←	Newton's third law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1430
`depends_on`	←	Parabolic trajectory	declared	parts/03-classical-mechanics/03-exp-projectile-motion.tex:95
`depends_on`	←	Equation of motion in a rotating frame	declared	parts/03-classical-mechanics/12-rigid-body-rotating-frames.tex:2153