k=0.1, ω=100 rad/s, I=5 A → E=10 V, T=0.5 N·m, P=50 W E=k·ω=0.1·100=10 V。T=k·I=0.1·5=0.5 N·m。P_mech=T·ω=E·I=50 W(E·I=10·5=50 W 验证机电功率平衡)。{"result":"DC motor back-EMF & torque. k=0.1 V·s/rad (N·m/A), ω=100 rad/s (954.9297 RPM), I=5 A. E = k·ω = 10 V. T = k·I = 0.5 N·m. P_mech = T·ω = E·I = 50 W.","metadata":{"input":{"k":0.1,"speed":100,"speedUnit":"rad_s","current":5},"result":{"motorConstant_k":0.1,"speed_rad_s":100,"speed_rpm":954.9297,"armatureCurrent_A":5,"backEmf_V":10,"torque_Nm":0.5,"mechanicalPower_W":50}}}
k=0.05, n=3000 RPM, I=10 A → E≈15.71 V, T=0.5 N·m, P≈157.08 W ω=3000·2π/60≈314.159 rad/s。E=0.05·314.159≈15.708 V。T=0.05·10=0.5 N·m。P_mech=T·ω≈157.08 W。{"result":"DC motor back-EMF & torque. k=0.05 V·s/rad (N·m/A), ω=314.1593 rad/s (3000 RPM), I=10 A. E = k·ω = 15.708 V. T = k·I = 0.5 N·m. P_mech = T·ω = E·I = 157.0796 W.","metadata":{"input":{"k":0.05,"speed":3000,"speedUnit":"rpm","current":10},"result":{"motorConstant_k":0.05,"speed_rad_s":314.1593,"speed_rpm":3000,"armatureCurrent_A":10,"backEmf_V":15.708,"torque_Nm":0.5,"mechanicalPower_W":157.0796}}}