definition 18.27 Angular position, velocity and acceleration

open in the book · parts/03-classical-mechanics/01-kinematics.tex:831 · p. 728

ground object -- no derivation owed

Rests on

depends_on definition 18.11 Acceleration ¶
- 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 18.10 Velocity ¶
  - depends_on definition 7.26 Derivative of a function at a point ¶ ↺
  - 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 18.9 Position ¶ ↺
depends_on definition 18.10 Velocity ¶ ↺

Supports

depends_on definition 18.29 Angular velocity vector ¶
- depends_on remark 18.30 The angular velocity is an element of $\mathfrak{so}(3)$ ¶
depends_on phenomenon 18.31 Uniform circular motion is accelerated motion ¶
- depends_on proposition 18.32 Tangential and centripetal components ¶
depends_on proposition 18.32 Tangential and centripetal components ¶ ↺
depends_on remark 18.28 The radian carries no dimension ¶

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`	→	Acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:846
`depends_on`	→	Position	declared	parts/03-classical-mechanics/01-kinematics.tex:846
`depends_on`	→	Velocity	declared	parts/03-classical-mechanics/01-kinematics.tex:846
`depends_on`	←	Angular velocity vector	declared	parts/03-classical-mechanics/01-kinematics.tex:879
`depends_on`	←	Uniform circular motion is accelerated motion	declared	parts/03-classical-mechanics/01-kinematics.tex:918
`depends_on`	←	Tangential and centripetal components	declared	parts/03-classical-mechanics/01-kinematics.tex:981
`depends_on`	←	The radian carries no dimension	declared	parts/03-classical-mechanics/01-kinematics.tex:858