Question

物理题求解答过程

1. Four small spheres (小球) are fastened (固定) to the ends of two rodsof lying in the xy plane. Assume the mass of the rod can be ignored, and theradii (半径) of the spheres are small compared (比较) with the dimensions (尺寸) of the rods.
(a) If the system rotates about y axis with an angular speed ω, find the momentof inertia and the rotational kinetic energy of the system aboutthis axis.
(b) If the system rotates in the xy plane about Z axis through the center ofsystem.
Find the moment of inertia and the rotationalkinetic energy about this axis.
What if? What if the mass M is much larger thanm? How do the answers to parts (a) and(b) compare?
四个小球被固定在xy平面上两个小棒的4端。假设小棒的质量可以被忽略，并且小球的半径很小与小棒的尺寸相比。
(a) 如果系统以角速度ω绕y轴旋转，求这个系统关于y轴的转动惯量(惯性矩)和转动动能？
(b) 如果系统在xy平面绕z轴旋转，且z轴穿过系统中心。求绕z轴的转动惯量和转动动能？
假使质量M远大于m，要怎么回答(a)和(b)的区别？
翻译可能有些许差异，但还是请各位大神帮忙解答下

Answer 1

看不清你的图片，我假设两个x轴上的球到原点的距离均为a，y轴上的两个球到原点距离均为b。
则对于a）
I=M*a^2+M*a^2=2*M*a^2
E=1/2*I*ω^2=M*a^2*ω^2
对于b）
I=2*m*b*^2+2*M*a^2
E=1/2*I*ω^2=(m*b*^2+M*a^2)ω^2
如果M>>m,则两道题的转动惯量和动能近似相等。