definition 19.5 Linear momentum

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:93 · p. 734

ground object -- no derivation owed

Rests on

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 3.43 Map ¶
  - 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 definition 18.3 Particle ¶ ↺

Supports

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 proposition 29.14 Angular momentum and kinetic energy ¶
  - depends_on theorem 19.58 Decomposition of the angular momentum ¶
    - 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 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 29.49 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 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 definition 19.55 Angular 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 27.14 Central motion ¶
    - depends_on definition 19.31 Energy ¶
      - depends_on proposition 27.20 Conservation of energy ¶
      - depends_on theorem 19.32 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 ¶
    - depends_on phenomenon 42.4 The lunar orbit is not polarized toward the Sun ¶
      - tests experiment Lunar laser ranging and Gravity Probe B ¶
  - 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 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 theorem 19.62 Rotational second law for a system ¶
    - 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 50.1 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 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 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 ¶ ↺

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`	→	Velocity	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:99
`depends_on`	→	Mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:99
`depends_on`	←	Translational equilibrium	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:65
`depends_on`	←	Angular momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:479
`depends_on`	←	Linear momentum of the centre of mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1523
`depends_on`	←	Newton's first law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:115
`depends_on`	←	Newton's second law	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:161