文档介绍：Chapters 10-11 Angular Momentum Plane Polar Coordinate System (平面极坐标系) O ? r ),(?rP r ???????r polar axis r ??? radial base vector transverse base vector Radial and transverse base vectors are not constant vectors. O ?????)( ?ttr??r ??)( ?tr????????rr ???????????????tt rrd dd d??)( ?tt??????)( ?t?rrtt ???????????????d dd d )( ?tr )( ?t?)( ?ttr??)( ?tt??? r ??? The change rates with time of and position vector rrr ????( ) ???? dr d r r v rr rr rr r dt dt ??? ? ????????? ? velocity ?vvv r????? The position, velocity, and acceleration in polar system rrv r??????????rv? radial velocity transverse velocity ??( ) ( ) ( ) r d v v dv d rr d r a dt dt dt dt ????? ? ??? ??????( )???? d rr rr rr rr r dt ??? ???????? ???? 2?( ) ??? d r r r r r dt ???? ???? ???? ???? r r??????????????? 22 ??( ) ( ) r a r r r r r a a ?? ???? ? ????? ??? ????? ? acceleration rrra r?)( 2????????????)2( ?????rra?? radial acceleration transverse acceleration Rotation: Linear and Angular variables ? rv d? ds ? ddt ??? ?????与成右手螺旋。??v ? dθ ds ds rd θ? angular displacement linear displacement angular velocity angular velocity is a vector ds d v r r dt dt ??? ?? v r ??? ??= right-hand rule angular acceleration ddt ???rrra r?)( 2????????????)2( ?????rra?? radial acceleration transverse acceleration constant r ? ? 22rv a r r a r ????? ?????? period 2 2 rTv ? ??? ? ic energy of rotation Particle: Particle system: 2 2 2 11 22 kk E mv E mr v r ?????? ????? 2 2 2 1 1 2 2 k i i i i i i i E mv m r ?? ?? ? If all the particles have the same angular velocity i ? ?? 2 2 2 2 1 1 2 2 k i i i i i i E m r m r ? ?? ??