2013年第30届全国中学生物理竞赛复赛试卷中第三题,试题及部分解答摘录如下:题目一质量为m、长为L的匀质细杆,可绕过其一端的光滑水平轴O在竖直平面内自由转动。杆在水平状态由静止开始下摆。(1)令λ=m L表示细杆质量线密度。当杆以角速度ω绕过其一端的光滑水平轴O在竖直平面内转动时,其转动动能可表示为Ek=kλαωβLγ式中,k为待定的没有单位的纯常数。已知在同一单位制 2013 third in the 30th National Secondary Physics Referees papers third questions, questions and answers to some of the answers are as follows: a quality of m, L for the uniform thin rod, smooth around one end of its smooth horizontal axis O in the vertical Straight plane free rotation. The lever starts to pendulum from rest in the horizontal state. (1) Let λ = m L denote the rod mass linear density. The rotational kinetic energy of the rod when it rotates in the vertical plane at a smooth horizontal axis O around its one end at angular velocity ω can be expressed as Ek = kλαωβLγ where k is a pure constant to be determined without a unit. Known in the same unit system