圆筒转动惯量公式微积分推导

题目

圆筒转动惯量公式微积分推导
如题为何公式是J=m/2*（r1*r1+r2*r2）中“r1*r1+r2*r2”为何不是减而是加

答案

J=∫r^2ρdv
=∫r^2ρdr*H*r*2pai
=ρ*H*2pai∫r^3dr
=ρ*H*2pai/4r^4(r2-→r1)
=[ρ*H*2pai]/4(r1^2-r2^2)(r1^2+r2^2)
=m/2(r1^2+r2^2)