definition 19.51 Linear momentum of the centre of mass

open in the book · parts/03-classical-mechanics/02-newtonian-dynamics.tex:1517 · p. 752

ground object -- no derivation owed

Rests on

depends_on definition 19.47 Position of the centre of mass ¶
- depends_on definition 19.39 Body ¶
  - depends_on definition 18.4 Body ¶
    - depends_on definition 18.3 Particle ¶
  - 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 18.3 Particle ¶ ↺
- depends_on definition 19.40 Total mass ¶
  - depends_on definition 19.39 Body ¶ ↺
  - depends_on definition 19.3 Mass ¶ ↺
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 ¶ ↺

Supports

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 ¶

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`	→	Position of the centre of mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1523
`depends_on`	→	Linear momentum	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1523
`depends_on`	←	Angular momentum of the centre of mass	declared	parts/03-classical-mechanics/02-newtonian-dynamics.tex:1681