What is the rotational energy of the blade at its operating

来源：学生作业帮编辑：作业帮分类：英语作业时间：2024/05/14 06:59:13

What is the rotational energy of the blade at its operating angular speed of 3470rpm?
A lawn mower has a flat, rod-shaped steel blade that rotates about its center. The mass of the blade is 0.65kg and its length is 0.55m .

线密度 a = m/l, m=0.65kg, l=0.55m
角速度 w = 3470*2pi/60 = 363.2 rad/s
动能K = 2*int (r=0->l/2) 1/2 a*dr * (w*r)^2 = m/l * w^2 * int(r=0->l/2) r^2 dr
= m/l * w^2 * (l/2)^3/3 = 1/24 * (m*l^2) * w^2 = 1080.7 J

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