扭矩例题解答
现在已知:一个直径是80mm的轴,长度为500mm,材料密度7.8吨/立方米。计算一下,当在0.1秒内使它达到500转/分的速度时所需要的力矩?
轴质量 m = Vρ = πr^2 * 0.5 * 7800 = 3900πr^2 kg;
转动惯量 J = mr^2/2 = 3900πr^2 * r^2/2 = 1950π * (0.04)^4 = 0.004992π kgm^2;
平均角速度 ω = 500/60 * 2π/2 = 25π/3 red/s
角动量 L = Jω = 0.004992π * 25π/3 = 0.0416π^2 kgm^2/s;
力矩 Mo = dL/dt = 0.0416π^2/0.1 = 0.416 * 3.14^2 = 4.1 Nm 。
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