postulate 19.1 Inertia

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:38 · p. 733

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 18.3 Particle ¶ ↺

Supports

depends_on definition 19.2 Interaction ¶
- 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 definition 19.3 Mass ¶
- depends_on definition 19.39 Body ¶
  - depends_on definition 19.47 Position of the centre of mass ¶
    - depends_on definition 27.6 Centre of gravity ¶
    - depends_on definition 19.51 Linear momentum of the centre of mass ¶
      - depends_on definition 19.55 Angular momentum of the centre of mass ¶
    - depends_on theorem 29.20 Parallel-axis theorem ¶
      - depends_on corollary 29.21 The centre of mass minimizes the moment ¶
  - depends_on definition 19.41 Moment of inertia about an axis ¶
    - depends_on definition 19.42 Inertia tensor ¶
      - depends_on definition 29.13 Inertia tensor, continuum form ¶
      - depends_on example 19.45 The uniform solid sphere ¶
      - depends_on proposition 19.43 The moment of inertia is a quadratic form in the axis ¶
    - depends_on theorem 19.44 Parallel axes; Steiner ¶
  - depends_on definition 19.40 Total mass ¶
    - depends_on definition 19.47 Position of the centre of mass ¶ ↺
  - depends_on definition 29.1 Rigid body ¶
    - depends_on proposition 29.2 Six degrees of freedom ¶
      - depends_on theorem 29.3 Euler's rotation theorem ¶
- depends_on definition 19.29 Kinetic energy ¶
  - 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 theorem 19.38 Work–energy theorem ¶
- depends_on definition 19.41 Moment of inertia about an axis ¶ ↺
- depends_on definition 19.5 Linear momentum ¶
  - depends_on definition 27.2 Translational equilibrium ¶
  - depends_on definition 19.18 Angular momentum ¶
    - depends_on definition 27.3 Rotational equilibrium ¶
    - depends_on definition 19.55 Angular momentum of the centre of mass ¶ ↺
    - 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 postulate 19.22 Newton's second law, rotational case ¶
      - depends_on theorem 29.25 Euler's equations ¶
    - depends_on proposition 19.20 For one particle the rotational first law is not independent ¶
  - depends_on definition 19.51 Linear momentum of the centre of mass ¶ ↺
  - depends_on postulate 19.6 Newton's first law ¶
    - depends_on phenomenon 19.7 Persistence of uniform motion ¶
    - depends_on postulate 19.19 Newton's first law, rotational case ¶ ↺
    - depends_on postulate 19.8 Newton's second law ¶
      - depends_on definition 19.30 Conservative force and potential energy ¶
      - depends_on definition 19.34 Work ¶
      - depends_on phenomenon 49.16 Pulsars: clocks at nuclear density ¶
      - depends_on phenomenon 42.1 Universality of free fall ¶
      - depends_on phenomenon 19.10 Force, mass and acceleration ¶
      - depends_on postulate 19.22 Newton's second law, rotational case ¶ ↺
      - depends_on postulate 19.48 Newton's third law ¶ ↺
      - depends_on theorem 20.2 Parabolic trajectory ¶
      - depends_on theorem 29.51 Equation of motion in a rotating frame ¶
    - depends_on proposition 19.20 For one particle the rotational first law is not independent ¶ ↺
  - depends_on postulate 19.8 Newton's second law ¶ ↺
- depends_on definition 19.40 Total mass ¶ ↺
- depends_on remark 19.11 Mass is a Galilean scalar ¶

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:42
`depends_on`	→	Particle	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:42
`depends_on`	←	Interaction	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:54
`depends_on`	←	Mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:64