转轴 转轴 2 转轴 × l 4 12
1 2 2 J mr = 转轴 1 2 4 J mr = 2 2 4 12 mr ml J = +
△O=(n→∞)=2n J=im R n→>00i h = lim ∑ 2 n→>4 (rsin 81) =mr- lim sin2△6+sin22△+…sin21|-△6+sin 100:1l 2 J==mr 项 2
2 1 lim n i i n i J m r → = = x y 0 R i i = ( ) 2 n n → = 2 i i n ( ) 2 1 4 lim sin 4 n i n i m r n → = = 2 2 2 2 2 1 1 lim sin sin 2 sin sin 2 2 n n i m r n → = = + + − + 1 2 n项 2 J mr =
最设任意物体某固定轴o的转动惯量为,绕 通过质心而平行于轴O的转动惯量为,则有 =y+md 2 J=∑m少2m(+1-201c0 ∑m2+∑md2
2 J J md = +c 设任意物体绕某固定轴O的转动惯量为J，绕 通过质心而平行于轴O的转动惯量为Jc，则有 R mi i ri d x C y θi O ( ) 2 2 2 1 1 2 cos n n i i i i i i i J m r m R d dR = = = = + − 2 2 1 1 1 2 cos n n n i i i i i i i i i m R m d d m R = = = = + − 1 n i i i m x = 0
由J=J+md2 =m+mR R 14转轴 2R 2 2 J=2lim 2 - i=142n / 2n 2 lim n→>0o 3 2 ml 12
m R 2 由J J md = +c 2 2 = + mR mR2 = 2mR 2 2 1 1 2 lim 4 2 2 2 n n i m m l J r i → = n n n = + 2 2 23 1 lim 4 4 n n i mr ml i → = n = + 2 2 4 12 mr ml = +