※ 引述《ib61632003 (北北)》之铭言： : 小弟有三题普物想请教 : 希望能有强者解答，要有计算过程和解释 : 1.A uniform thin wire is bent into a semicircle of radius r. Determine : the coordinates of its center of mass with recpect to an origin of coordinates : at the center of the ''full'' circle. 因为the thin wire is uniform 根据点对称性质..可知圆线质心在几何中心处.. 将圆座标设为几何中心处.. 令质块δm位置向量与半圆中段位置向量的夹角为θ..设线密度为α.. 根据面对称性质..半圆质心会位於几何中心与半圆中段之间的位置.. 则质心距与几何中心位置距离为.. ∫(-π/2→π/2) (ρ*r*δθ)*(r*cosθ) / ρ*π*r = 2*R0/π : 2.A centrifuge rotor is accelerated from rest to 2000 rpm in 30s. : (a) What is its average angular acceleration? (b) Through how many : revolutions has the centrifuge rotor turned during its acceleration period, : assuming constant angular acceleration? 2000 rpm = (200*π/3) rad/s α(average) = (200*π/3)/30 = (20*π/9) rad/s^2 根据angular acceleration is constant 设旋转数为N..则 N = 2000*(30/60)*(1/2) = 500 : 3.A bullet of a mass m moving with velocity v strikes and becomes : embedded at the edge of a cylinder of mass M and radius R0. The cylinder, : initially at rest ,begins to rotate about its symmetry axis,which remains : fixed in position.Assuming no frictional torque,what is the angular velocity : of the cylinder after this collision?What is the change in kinetic energy? 假设圆柱是均匀的..设体密度为ρ..高度为h.. 设symmetry axis为旋转轴之转动惯量 I(cyl)..则 I(cyl) = ∫(0→R0) (2*π*r*δr)*ρ*h*r^2 = ρ*π*R0^4*h/2 = M*R0^2/2............................(a) 设angular velocity为ω 根据角动量守恒 m*v*R0 = [I(cyl) + m*R0^2]*ω 将(a)代入上式解得 ω = m*v*/{[(M/2)+m]*Ro} 设the change in knetic energy为ΔE 则ΔE = (1/2)*m*v^2 - (1/2)*[I(cyl) + m*R0^2]*ω^2 = (1/2)*m*v^2*{1-m/[(M/2)+m]} : 感谢耐心阅读 : 谢谢回答 : 微薄P币以表心意 --

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