利用恒力矩转动法验证刚体转动惯量正交轴定理

Verifying the perpendicular axis theorem of rotational inertia of rigid body using a constant-torque rotational method

利用恒力矩转动法测量了自制的不锈钢矩形薄板状样品的转动惯量.沿长、宽,和垂直于板面3个方向的转动惯量分别是7.70×10^(-4) kg·m^2,3.23×10^(-3) kg·m^2和3.97×10^(-3) kg·m^2.沿长、宽方向的转动惯量之和基本等于垂直于板面方向的转动惯量,相对偏差仅为0.84%,验证了刚体转动惯量正交轴定理.分析了由薄板厚度对长、宽方向的转动惯量贡献不超过5‰,在实验中无须考虑厚度的影响.测量结果表明:固定螺丝、定位销对测量结果影响不大.此外还分析了空气阻尼、塔轮半径和砝码质量等因素对实验结果的影响.

The moment of inertia of a self-made stainless sheet with rectangle shape had been measured using a constant-torque rotational method. The experimental data were 7.70×10^-4 kg · m^2 and 3.23×10^-3 kg·m^2 for the rotational axis parallel to long and short edge of sheet, respectively, and 3.97×10^3kg·m^2 for the rotation axis vertical to the surface of plate. The sum of the moment of inertia along the long and short edge of the sheet was approximately equal to that along the surface normal of the sheet. The relative error was about 0.84%, perfectly proved the perpendicular axis the- orem. It was also shown that the improvement of the moment of inertia by considering the thickness of the sheet was less than 5‰, then it was reasonable to omit the effect of thickness. The experimen- tal results indicated the screws and dowel pin played no important role. Moreover, the effects of air damping, radius of cone pulley and mass of weights were discussed.