理论力学全套解疑09

9-1(a)ABABAB9-1AB9-1(b)ABA1B1A(B)AA1BB1O(O1)OA(O1B)9-4OAO1BMABr9-59-59-6OABAB′B9-6BaBτAaAAs=RϕAϕRsaA==BϕτRaB=BBBAaaa≠=τB′B′B′BBBBϕOxxϕ=ϕ(t)x=x(t)tddϕω=txvdd=22ddddttωωε==22ddddtxtva==ϕ=ωtx=vtω=ω0+εt2021ttεωϕ+=εϕωω2202+=tv=v0+at2021tatvx+=axtvv2202+=ϕωεxvav=Rωϕρ=vv=Rωϕρ=v9-8MMrrρirr=ρijiiiirvϕρρρρρ+=+===ttttdddd)(ddddiρMvρjϕρMvϕM2222)(ϕρρϕρ+=+=vvvϕρϕ=vM9-89-9vM=ωrrMωωMω=18(rad/s)OAOAAOxyz104080201010MvMmm9-91OA222804010++==90989080cos949040cos919010cos======γβα)rad/s(168298949118)coscos(cos||kjikjikji++=⎟⎠⎞⎜⎝⎛++=++=γβαωω2MMr=20i10j+10kMvM=ωr=(2i+8j+16k)(20i10j+10k)=240i+300j180kmm/svM424180300240222=++=Mvmm/snωnn/n(r/min)ωω/ω(rad/s)30π60π2nn=⋅=ω