1

x_com = m₁x₁ + m₂x₂m₁ + m₂x_com = 1M Σ m_ix_ir_com = 1M Σ m_ir_iM = Σ m_i

2

rcom = 1M∫ r dmrcom = 1V∫ r dV  (ρ = )xcom = 1M∫x2x1 xλ dx = 12(x1 + x2)

3

Mv_com = Σ m_iv_iMa_com = Σ m_ia_i = Σ F_iF_net = Ma_com = Md²r_comdt²

4

p = mvF = dpdtP = Σ pi = MvcomΔp = J = ∫tfti F(t) dt

5

F_net = dPdt = 0 ⇒ P = F₂₁ = −F₁₂m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′

6

v′ = m₁m₁ + m₂v₁ + m₂m₁ + m₂v₂ = v_comΔK = −m₁m₂(v₁ − v₂)²2(m₁ + m₂) ≤ 0

7

v₁ + v₁′ = v₂ + v₂′v₁′ = m₁ − m₂m₁ + m₂v₁ + 2m₂m₁ + m₂v₂v₂′ = 2m₁m₁ + m₂v₁ + m₂ − m₁m₁ + m₂v₂

8

p_1i + p_2i = p_1f + p_2fK_1i + K_2i = K_1f + K_2f  ()

9

Mv = (M + dM)(v + dv) − dM U−dM v_rel = M dvRv_rel = Ma = Tv_f − v_i = v_rel lnM_iM_f