Acentrifugerotorrotatingat11000isshutoffandiseventuallybroughtuniformlytorestbyafrictionaltorqueof2.03.Ifthemassoftherotoris4.98anditcanbeapproximatedasasolidcylinderofradius0.0300,throughhowmanyrevolution

Question

A centrifuge rotor rotating at 11000 is shut off and is eventually brought uniformly to rest by a frictional torque of 2.03 .If the mass of the rotor is 4.98 and it can be approximated as a solid cylinder of radius 0.0300 ,through how many revolutions will the rotor turn before coming to rest?

Answer 1

实心盘转动惯量：J=mR²
具有的初始转动动能 转化为 阻力矩做功：1/2Jω²=Tθ
转动圈数：n=θ/(2π)
代入：m=4.98,R=0.03,ω=11000,T=2.03
解得：
J=0.004482
θ=133577.
n=21259.4
如果原题有单位且不统一,则先统一后再代入算.