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一般的な関係式

 意  味       並 進 運 動   回 転 運 動 


運動を変える作用          F            N ≡r×F


  勢 い        p ≡ mv            L≡r×p

                      d                  d
 運動方程式       F =         p     N=           L
                      dt                 dt


回転軸を固定させた場合

  意 味       並 進 運 動   回 転 運 動 


  座 標            x[m]              θ[rad]

                 dx                 dθ
  速 さ       v≡      [m/s]     ω≡       [rad/s]
                 dt                 dt
                 dv             dω
  加 速       a≡      [m/s2 ]   α≡    [rad/s2 ]
                 dt              dt
                                 ∑
  慣 性            m[kg]        I≡           2
                                      mj r j
                                     j


  勢 い        p ≡ mv                L ≡ Iω

                      d2                 d2
 運動方程式      F =m          x    N =I          θ
                      dt2                dt2
                   1                     1 2
運動エネルギー      K≡      mv 2     KR ≡         Iω
                   2                     2

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剛体運動(並進運動と回転運動の対比)

  • 1. 一般的な関係式 意  味  並 進 運 動   回 転 運 動  運動を変える作用 F N ≡r×F 勢 い p ≡ mv L≡r×p d d 運動方程式 F = p N= L dt dt 回転軸を固定させた場合 意 味  並 進 運 動   回 転 運 動  座 標 x[m] θ[rad] dx dθ 速 さ v≡ [m/s] ω≡ [rad/s] dt dt dv dω 加 速 a≡ [m/s2 ] α≡ [rad/s2 ] dt dt ∑ 慣 性 m[kg] I≡ 2 mj r j j 勢 い p ≡ mv L ≡ Iω d2 d2 運動方程式 F =m x N =I θ dt2 dt2 1 1 2 運動エネルギー K≡ mv 2 KR ≡ Iω 2 2