definition 18.11 Acceleration

open in the book · parts/03-classical-mechanics/01-kinematics.tex:277 · p. 721

ground object -- no derivation owed

Rests on

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 3.24 Quantifiers ¶
      - depends_on definition 3.28 Set ¶
- 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 ¶

Supports

depends_on definition 18.27 Angular position, velocity and acceleration ¶
- 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 ¶
depends_on lemma 27.15 Velocity and acceleration in plane polar coordinates ¶
depends_on phenomenon 18.31 Uniform circular motion is accelerated motion ¶ ↺
depends_on phenomenon 18.12 Uniformly accelerated motion ¶
- depends_on phenomenon 20.1 phen:parabolic-trajectory ¶
  - assumes experiment Absolute Ballistic Gravimetry (1995–present) ¶
  - 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 ¶
  - tests experiment Galileo's Inclined Planes ¶
depends_on proposition 18.33 Intrinsic decomposition of the acceleration ¶
- depends_on remark 18.34 The two ways an acceleration can be zero ¶
depends_on proposition 18.23 Transformation of velocity and acceleration ¶
- depends_on phenomenon 18.26 Composition of velocities, and its limit ¶

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`	→	Derivative of a function at a point	declared	parts/03-classical-mechanics/01-kinematics.tex:283
`depends_on`	→	Velocity	declared	parts/03-classical-mechanics/01-kinematics.tex:283
`depends_on`	←	Angular position, velocity and acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:846
`depends_on`	←	Velocity and acceleration in plane polar coordinates	declared	parts/03-classical-mechanics/10-central-forces-statics.tex:419
`depends_on`	←	Uniform circular motion is accelerated motion	declared	parts/03-classical-mechanics/01-kinematics.tex:918
`depends_on`	←	Uniformly accelerated motion	declared	parts/03-classical-mechanics/01-kinematics.tex:327
`depends_on`	←	Intrinsic decomposition of the acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:1033
`depends_on`	←	Transformation of velocity and acceleration	declared	parts/03-classical-mechanics/01-kinematics.tex:709