sim_subset/circular/7/formula_info.json

{
  "correct_letter": "A",
  "correct_formula": "(1/2)·m·v_0² + m·g·R·(1-cosθ_start) = (1/2)·m·v² + m·g·R·(1-cosθ)",
  "annotation": "Environment: g=-9.81, F_drag=0.0\nGround: mu_s=0.0, mu_k=0.0\nTireSphere: d = 1.0, e = 0.6, theta_start = 270°, v_0 = 2.0\nStyrofoamSphere: d = 1.0, e = 0.15, theta_start = 270°, v_0 = 5.0\nTrack_0: R = 2.0, e = 0.3, theta_min = 270°, theta_max = 360°, mu_s = 0.0, mu_k = 0.0",
  "choices": [
    "(1/2)·m·v_0² + m·g·R·(1-cosθ_start) = (1/2)·m·v² + m·g·R·(1-cosθ)",
    "F = (3/4)·E*·√(R·d³)",
    "F_N = m·g·(cosθ - 2) + m·v²/R",
    "v = f·λ"
  ],
  "correct_index": 0,
  "physics_type": "Circular",
  "seed": "Circular|benchmark/circular/7"
}