theorem 19.63 The spin obeys the same law about the centre of mass

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:1881 · p. 756

Rests on

depends_on lemma 19.57 The centre of mass is the origin of its own frame ¶
- depends_on equation 19.38 eq:newt-cm-position ¶
- depends_on equation 19.49 eq:newt-cm-relative ¶
- proves proof ch:02-newtonian-dynamics@proof-18 ¶
depends_on postulate 19.61 Newton's third law, strong form ¶
- depends_on corollary 19.14 Central pair forces are admissible ¶
  - depends_on proposition 19.13 Which forces are admissible ¶
    - depends_on definition 18.18 Galilean transformation ¶
      - depends_on definition 18.8 Inertial frame of reference ¶
      - depends_on postulate 18.14 Absolute time ¶
      - depends_on postulate 18.16 Principle of Galilean relativity ¶
    - depends_on theorem 19.12 Galilean covariance of the second law ¶
      - depends_on definition 18.18 Galilean transformation ¶ ↺
      - depends_on equation 19.4 eq:newt-fma ¶
      - depends_on postulate 18.14 Absolute time ¶ ↺
      - proves proof ch:02-newtonian-dynamics@proof-3 ¶
    - proves proof ch:02-newtonian-dynamics@proof-4 ¶
- depends_on postulate 19.48 Newton's third law ¶
  - depends_on definition 19.2 Interaction ¶
    - depends_on definition 18.3 Particle ¶
    - depends_on postulate 19.1 Inertia ¶
      - depends_on definition 18.8 Inertial frame of reference ¶ ↺
      - depends_on definition 18.3 Particle ¶ ↺
  - depends_on postulate 19.8 Newton's second law ¶
    - depends_on definition 19.5 Linear momentum ¶
      - depends_on definition 18.10 Velocity ¶
      - depends_on definition 19.3 Mass ¶
    - 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 ¶ ↺
depends_on theorem 19.58 Decomposition of the angular momentum ¶
- depends_on definition 19.55 Angular momentum of the centre of mass ¶
  - depends_on definition 19.18 Angular momentum ¶
    - depends_on definition 18.3 Particle ¶ ↺
    - depends_on definition 19.5 Linear momentum ¶ ↺
  - depends_on definition 19.51 Linear momentum of the centre of mass ¶
    - depends_on definition 19.47 Position of the centre of mass ¶
      - depends_on definition 19.39 Body ¶
      - depends_on definition 19.40 Total mass ¶
    - depends_on definition 19.5 Linear momentum ¶ ↺
- depends_on equation 19.44 eq:newt-cm-momentum ¶
- depends_on lemma 19.57 The centre of mass is the origin of its own frame ¶ ↺
- proves proof ch:02-newtonian-dynamics@proof-19 ¶
proves proof ch:02-newtonian-dynamics@proof-22 ¶

Supports

depends_on phenomenon 19.65 Spin is conserved when no external torque acts ¶
depends_on theorem 19.68 Conservation of angular momentum ¶

Neighborhood

Every logical edge within two steps of this node.

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Edges

type	direction	node	provenance	where
`depends_on`	→	The centre of mass is the origin of its own frame	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1893
`depends_on`	→	Newton's third law, strong form	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1893
`depends_on`	→	Decomposition of the angular momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1893
`depends_on`	←	Spin is conserved when no external torque acts	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1950
`depends_on`	←	Conservation of angular momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:2061
`proves`	←	ch:02-newtonian-dynamics@proof-22	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1897