definition 19.3 Mass

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:60 · p. 733

ground object -- no derivation owed

Rests on

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 18.3 Particle ¶ ↺
  - depends_on definition 18.6 Free particle ¶
    - depends_on definition 18.3 Particle ¶ ↺
- depends_on definition 18.3 Particle ¶ ↺

Supports

depends_on definition 19.39 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 proposition 29.14 Angular momentum and kinetic energy ¶
      - depends_on theorem 19.58 Decomposition of the angular momentum ¶
  - 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 definition 29.19 Inertia ellipsoid ¶
      - depends_on example 29.23 The polar moment of the Earth, and what it reveals ¶
      - depends_on proposition 49.17 Magnetic-dipole spin-down ¶
      - depends_on proposition 29.14 Angular momentum and kinetic energy ¶ ↺
      - depends_on proposition 29.15 Positivity ¶
      - depends_on proposition 29.24 MacCullagh's formula ¶
      - depends_on proposition 29.22 Perpendicular-axis theorem ¶
      - depends_on theorem 29.20 Parallel-axis theorem ¶ ↺
      - depends_on theorem 29.16 Principal axes ¶
    - 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 notation 29.9 The $z$–$x$–$z$ Euler angles used in this treatise ¶
      - depends_on proposition 125.2 Crystallographic restriction ¶
      - depends_on proposition 29.8 Chasles: the general displacement is a screw ¶
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 proposition 29.36 Three first integrals ¶
      - depends_on theorem 27.10 Lagrange–Dirichlet ¶
- 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 remark 20.14 Why the elementary argument gives three halves of this ¶
  - 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 29.31 The intermediate-axis instability ¶
      - depends_on proposition 29.26 The two integrals of torque-free motion ¶
      - depends_on proposition 29.28 Free rotation of a symmetric body ¶
      - depends_on proposition 24.41 The free rigid body is a Lie–Poisson system ¶
  - 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 27.13 Central force ¶
      - depends_on definition 19.31 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 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 ¶
      - depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶
    - 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 phenomenon 19.50 Recoil and the conservation of momentum ¶
      - depends_on postulate 19.49 Net internal force ¶
      - depends_on postulate 19.61 Newton's third law, strong form ¶
      - depends_on theorem 27.30 Reduction of the two-body problem ¶
      - depends_on theorem 19.52 The centre of mass moves as a particle ¶
    - depends_on theorem 20.2 Parabolic trajectory ¶
      - depends_on corollary 20.3 Range, apex, time of flight ¶
      - 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 ¶ ↺
- 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`	→	Particle	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:64
`depends_on`	→	Inertia	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:64
`depends_on`	←	Body	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1175
`depends_on`	←	Kinetic energy	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:815
`depends_on`	←	Moment of inertia about an axis	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1225
`depends_on`	←	Linear momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:99
`depends_on`	←	Total mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1187
`depends_on`	←	Mass is a Galilean scalar	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:295