definition 19.18 Angular momentum

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:472 · p. 738

ground object -- no derivation owed

Rests on

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 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 ¶ ↺

Supports

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 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 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`	→	Particle	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:479
`depends_on`	→	Linear momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:479
`depends_on`	←	Rotational equilibrium	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:75
`depends_on`	←	Angular momentum of the centre of mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1681
`depends_on`	←	Newton's first law, rotational case	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:494
`depends_on`	←	Newton's second law, rotational case	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:590
`depends_on`	←	For one particle the rotational first law is not independent	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:504