求半径为 [tex=0.571x0.786]HXNXn3AXpwdIpZt8+6oCEw==[/tex]的球体对过球心的直线及对与球体相切的直线的转动惯量.

2022-05-30

求半径为 [tex=0.571x0.786]HXNXn3AXpwdIpZt8+6oCEw==[/tex]的球体对过球心的直线及对与球体相切的直线的转动惯量.

答案：

(1)取球心为原点,且取过球心的直线为[tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex]轴,则球为[tex=9.071x1.429]aG9HXa9s7wVoFSbMRa7CFCUTB85yL8xikUK8s5XYY6CO21Sjvtp7PGJt2TcdKT1DI8X7cqyPiiFASQa/jX4bIg==[/tex]取密度[tex=3.071x1.214]8R0wLc8gqkRjZi8MVVxoDw==[/tex]上任意一点[tex=3.214x1.357]8sXOVKPrSl7odQ08YRvxPw==[/tex]到[tex=0.5x0.786]C7x+w8+jOPZzxFrGGne6Dw==[/tex]轴 (转动轴)的距离的平方为[tex=13.857x1.5]PJ8mXryrapFWOqz1pSbaLimGQKAfptxFZMC8fG78bXUYixEIQU6FRPieNC8KJHSa[/tex], 故[tex=9.214x2.643]iAjCLziBzyA311OQLRK0gaoQ/+mkOkM2li2UhI+B55YvGJYD1GRr3RN42u8d9v3ajW506D8kUlI9MYMtbOuWRORy0hhCb85CC5J0HAupZdY=[/tex][tex=30.286x5.786]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[/tex][tex=15.071x2.929]rAHvFR5TG0KcD46+u1TZ25z2za1BrUFeplHnNenTQhV3QAyo2Ezjff9GaZXp9x+jJCb82GZ9RSz0EORcWjaLpsxB0HqxQ5/Tu1oh1KFYuLTlu4N4Dzv+JNhBPKRXWVNaPX+3CxN/8hJfqtAKdcgEfg==[/tex]  ([tex=4.357x2.357]Qp7Gm6HlNxDQ8IcoXNL01vJk/PAWXQWzjM/ATl862LI=[/tex]为球质量）(2)取球心为原点,且取与球体相切的直线 [tex=0.357x1.0]5vVfAZliYwqMw8JaLE+iEA==[/tex]为过点 [tex=3.214x1.357]vc7giHUQIZUeFRh39RDWtQ==[/tex]与[tex=0.5x0.786]gdMkE6SnyZedYLxpUxdkaQ==[/tex]轴平行的直线，则[tex=0.643x1.0]phUlpt1yUjl9gkO1jpA0Lg==[/tex]上任一点的坐标为[tex=3.214x1.357]fsktOJiklvwTXehG6HnYWw==[/tex]，它到球内任一点 [tex=3.214x1.357]8sXOVKPrSl7odQ08YRvxPw==[/tex]的距离平方为[tex=15.571x1.5]sp4z8ilZSsBWY5F5ljYitjfbuC8tfz3ZACOIr5QoDr0UEkjheWee5fpjjHJ0NPXp[/tex][tex=23.214x11.357]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[/tex][tex=19.143x5.214]Ck4j1YFlvVH5wCAykOEMi5Y9c4vFXHBYbWErKlomiFNxAkm830TlN39q45Tw4/M/ECjvDmX8SawWPHTx2RL6VxE7tPM0+Biwsned8h4BBInfxdMH1vH5AbTTAwUcFIqFPT5RQRD96SdCum+f6SiCYzce7zCcgApKs2BSSph3U5fJBoFXE3tB4Vh7WrLLtXoNrE0m9xx6WyqK1oCEh3+C1hY5OKKMHE6d2zzS4Pludp1QTR7NVS67EUJT4ZBqqYM0wIi8g3ChfjwTobIfyWp3C/tGcG2RAKiW8RSjyJUu3G8=[/tex]

举一反三

内容

0
球心在原点、半径为[tex=0.786x1.286]yokTf2U2Z7kNGUXMm22GjQ==[/tex]的球体，在其上任意一点的密度的大小与这点到球心的距离成正比，求这球体的质量。
1
无限大导电平面上有一导电半球, 半径为[tex=0.571x0.786]HXNXn3AXpwdIpZt8+6oCEw==[/tex], 在半球体正上方距球心及导电平面 [tex=0.643x1.0]uPu/UBwxTDghY6MHYDLmcA==[/tex] 处有一点电荷[tex=0.5x1.0]jedlXyMYwmfVwxRj2j9sSw==[/tex], 求该点电荷所受的力。[br][/br][img=279x226]17cfb4d0a6d07fc.png[/img]
2
在球心为[tex=0.786x1.0]5SeCOJOzMwSNbX8MGx2Qsg==[/tex]半径为[tex=0.571x0.786]HXNXn3AXpwdIpZt8+6oCEw==[/tex]、电荷体密度为[tex=0.571x1.0]wZfDAQ5tsV00QsfoitgWPw==[/tex]的均匀带电球体内偏心挖去一个半径为[tex=0.429x1.0]Q2fWySASH/4Xf2eu85OwAQ==[/tex]的小球(球心为[tex=1.071x1.143]MmXixlJTcz/ibZvmAVtYcg==[/tex])，如图所示，求[tex=0.786x1.0]XhVNsLJz3AkjM19LvAbO7w==[/tex]， [tex=3.214x1.357]vVrYqH4+1pK5N10DOjt2XAAPads1AgcKCAiI9zzWFSA=[/tex]各点的电势。[img=355x260]17a045dfb3aefd1.png[/img]
3
在球心位于原点、半径为 [tex=0.571x0.786]HXNXn3AXpwdIpZt8+6oCEw==[/tex]的均匀半球体靠圆形平面的一旁，拼接一个半径与球的半径相等、材料相同的均匀圆柱体，使拼接后的重心位于球心，试确定圆柱体的长.
4
球心在原点，半径为[tex=0.786x1.0]as0RCzgUx1oS48cKHRAVVg==[/tex]的球体，在其上任意一点的密度的大小与这点到球的距离成正比，求这球体的质量。