definition 18.3 Particle

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Supports

• depends_on definition 18.4 Body ¶
  • depends_on definition 19.39 Body ¶
    • depends_on definition 19.47 Position of the centre of mass ¶
      • depends_on definition 27.6 Centre of gravity ¶
      • depends_on definition 19.51 Linear momentum of the centre of mass ¶
        • depends_on definition 19.55 Angular momentum of the centre of mass ¶
      • depends_on theorem 29.20 Parallel-axis theorem ¶
        • depends_on corollary 29.21 The centre of mass minimizes the moment ¶
    • depends_on definition 19.41 Moment of inertia about an axis ¶
      • depends_on definition 19.42 Inertia tensor ¶
        • depends_on definition 29.13 Inertia tensor, continuum form ¶
        • depends_on example 19.45 The uniform solid sphere ¶
        • depends_on proposition 19.43 The moment of inertia is a quadratic form in the axis ¶
      • depends_on theorem 19.44 Parallel axes; Steiner ¶
    • depends_on definition 19.40 Total mass ¶
      • depends_on definition 19.47 Position of the centre of mass ¶ ↺
    • depends_on definition 29.1 Rigid body ¶
      • depends_on proposition 29.2 Six degrees of freedom ¶
        • depends_on theorem 29.3 Euler's rotation theorem ¶
  • depends_on remark 18.5 rem:kin-body-refined ¶
• depends_on definition 18.7 Frame of reference ¶
  • depends_on definition 18.8 Inertial frame of reference ¶
    • depends_on definition 27.16 Areal velocity ¶
    • depends_on definition 18.18 Galilean transformation ¶
      • depends_on proposition 18.20 The Galilean group ¶
        • depends_on corollary 18.24 Galilean composition of velocities ¶
        • depends_on remark 18.22 Superseded, and in exactly what sense ¶
      • depends_on proposition 18.21 Galilean invariants ¶
        • depends_on remark 18.22 Superseded, and in exactly what sense ¶ ↺
      • depends_on proposition 18.23 Transformation of velocity and acceleration ¶
        • depends_on phenomenon 18.26 Composition of velocities, and its limit ¶
      • depends_on proposition 19.13 Which forces are admissible ¶
        • depends_on corollary 19.14 Central pair forces are admissible ¶
      • depends_on remark 18.19 Why the map is affine, and what is assumed to make it so ¶
      • depends_on remark 19.11 Mass is a Galilean scalar ¶
      • depends_on theorem 19.12 Galilean covariance of the second law ¶
        • depends_on proposition 19.13 Which forces are admissible ¶ ↺
        • depends_on theorem 19.25 Galilean covariance of the rotational second law ¶
      • depends_on theorem 19.25 Galilean covariance of the rotational second law ¶ ↺
    • depends_on phenomenon 18.17 Uniform motion is undetectable from within ¶
      • depends_on remark 18.13 Absolute space is stated here, and not adopted ¶
    • depends_on postulate 19.6 Newton's first law ¶
      • depends_on phenomenon 19.7 Persistence of uniform motion ¶
      • 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 postulate 19.8 Newton's second law ¶
        • depends_on definition 19.30 Conservative force and potential energy ¶
        • depends_on definition 19.34 Work ¶
        • depends_on phenomenon 49.16 Pulsars: clocks at nuclear density ¶
        • depends_on phenomenon 42.1 Universality of free fall ¶
        • depends_on phenomenon 19.10 Force, mass and acceleration ¶
        • depends_on postulate 19.22 Newton's second law, rotational case ¶
        • depends_on postulate 19.48 Newton's third law ¶
        • depends_on theorem 20.2 Parabolic trajectory ¶
        • depends_on theorem 29.51 Equation of motion in a rotating frame ¶
      • depends_on proposition 19.20 For one particle the rotational first law is not independent ¶
    • depends_on postulate 19.1 Inertia ¶
      • depends_on definition 19.2 Interaction ¶
        • depends_on postulate 19.48 Newton's third law ¶ ↺
      • depends_on definition 19.3 Mass ¶
        • depends_on definition 19.39 Body ¶ ↺
        • depends_on definition 19.29 Kinetic energy ¶
        • depends_on definition 19.41 Moment of inertia about an axis ¶ ↺
        • depends_on definition 19.5 Linear momentum ¶
        • depends_on definition 19.40 Total mass ¶ ↺
        • depends_on remark 19.11 Mass is a Galilean scalar ¶ ↺
  • depends_on definition 18.1 Motion and rest ¶
  • depends_on definition 18.9 Position ¶
    • 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 definition 18.1 Motion and rest ¶ ↺
    • depends_on definition 18.10 Velocity ¶
      • depends_on definition 18.11 Acceleration ¶
        • depends_on definition 18.27 Angular position, velocity and acceleration ¶ ↺
        • 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 proposition 18.33 Intrinsic decomposition of the acceleration ¶
        • depends_on proposition 18.23 Transformation of velocity and acceleration ¶ ↺
      • depends_on definition 18.27 Angular position, velocity and acceleration ¶ ↺
      • depends_on definition 18.29 Angular velocity vector ¶ ↺
      • depends_on definition 19.29 Kinetic energy ¶ ↺
      • depends_on definition 19.5 Linear momentum ¶ ↺
      • depends_on lemma 27.15 Velocity and acceleration in plane polar coordinates ¶ ↺
      • depends_on proposition 18.23 Transformation of velocity and acceleration ¶ ↺
• depends_on definition 18.6 Free particle ¶
  • depends_on definition 18.8 Inertial frame of reference ¶ ↺
• depends_on definition 18.9 Position ¶ ↺
• depends_on definition 19.18 Angular momentum ¶
  • depends_on definition 27.3 Rotational equilibrium ¶
  • depends_on definition 19.55 Angular momentum of the centre of mass ¶ ↺
  • depends_on postulate 19.19 Newton's first law, rotational case ¶ ↺
  • depends_on postulate 19.22 Newton's second law, rotational case ¶ ↺
  • depends_on proposition 19.20 For one particle the rotational first law is not independent ¶ ↺
• depends_on definition 19.2 Interaction ¶ ↺
• depends_on definition 19.3 Mass ¶ ↺
• depends_on definition 19.34 Work ¶ ↺
• depends_on postulate 19.1 Inertia ¶ ↺