-wwo。 l6.6 L无cURE#5 MOMENT UM ANGULAR MOMENTUM 0 YNAMICs OF丹sysT∈ M oF PARTICLES
FURTHER BASICS LINEAR MoMENTUM p会m NE认ToN'SLA 工F P CDN STANT Wow TAKE THE MOMENT OF MOMENTUM (ANGULAR MOMENTUM) MUST EXPLICITLY DEFINE A POWT ABOUT WHICH WE TAKE THE MOMENT LET He Fxp lAIN P) PERPENOICULA& To F TMES MpMENT ARM FI DEFINE TME MDMENT OR TOKQUE ABOVTo WITu FORCES F APPLIED TO M( CoNSTAAT) °x户卞x(F2)。FxF “x BKmH4T王(六×x) F×产工 (产xFx) d F d七
·50,TF =0.E Co小 STANT, 5- ANGULAR MoMENTUM UNCHANGED WHEN M=O APPuED MoMENT TIMe RATE of CHANGE of H woRK DoNE By A FoRCE ON A PARTCLE 户 FoRCE COMPONENT DIRECT MoTIDN NOTES: g ar=r dt rd七 G)CAN SIMPLIFy .产王SNCE (子三 FPx。2 了 d七 产) A 七 M V (KINETIC ENERGy) DENOTE As &K ONE EQUALs 惑-T4 THE工 NcREAsE T小 K|NETc小ERY
c小sER丹 TIVE FORcE 5-3 WoRK DONE ONL DEPENDS ON ENO-PoINTs No0N叫E? TH TA KEN F dr -d' AN Ex AcT DFFERENTIA ~PoE心 TIAL ENER B D NOW HAVE Fr A 4-V 0RsE工 POTENTIAL ENERG工SEAL TDE凵0RK00Ng cbA6u心 RESULT5 = A-8 8+1 T + E CALLEo THE PRINCIPLE OFCONSERVATIoN F MECH ANICAL E小ERGY ONLY APPLIEs FoR SYSTEMS TN A CONSERⅤ ATIVE FoACE FIEL0 MUCH MORE ON ENERGY METHODS LATER
5 OYNAMICS of A SYSTEM of PARTICLES GENERALIZE SINGLE PA RTICLE To MANy - STEPPING STONE TO RIGID B°0ˇ DYNAmIcS SIMILAR To PREVIOUS R∈svT,∈XcEP7No WE MUST A CCOUNT FoR THE INTERNAL INTERACTIONS OF THE PARTICLES N PARTICLES W\TH MAssEs M INERTIAL B 工 TERNAL FRAME ANO EXTERN AL FORCES 0RGF工 NENTAL RA惦 EXAMPLES。F乐升cM NEWTON'S 3 LAw f E 0 OTE PARALLE L 0(÷;-6)
· HAT CHANGES WHEN WE GO F尺MA SINGLE PARTICLE To MANY PARTICLES INTRodUCE CONCepT oF THE CENTER oF MASS FoR A SySTEM 88 →F0R&KPTE叶FWE SYSTEM,CA可U6 T TREA7s mHEC.0A.升CT小G0 ER THE EXTERNAL FREes MOMEN TUM ANGULAr MOMENTUM FoRces ToR&vEs AND THEIr RELATION SHI Ps 0o NoT CHANGE ENERGY CONCEPTS CAN GET VERy CoMPLEX IF THE INTERNAL FDRCES ARe NOT CDN SERVAT IVE
5-6 MOMENTVM OF MASS TS TOTAL SYSTEM MOMENTUM IS M;『; ANGULAR MoMEAT UM (A UT o)Is x(嗍 TOTAL SYSTEM ANGULAR MOMENTVM (ABOUT o)IS Σh,=2的;(x No SURPRISES DEFINE0 To BE THE POINT G\VEN By 会山∑m 的≡2 LET THEN WHY →ΣM; RELATIe To A FRAME ATTACH TO THE C D.M., SYSTEM MOMEMENTUM 工SzER0
57 RCES AND ToRQUES E众υATUN 0FMoT1 A FoR MAss i巧: Mf s fi+2f SUM FOR ALL PARTICLES + WHY BUT WE K№DnT 乙 三心 →EQ s of MOTION FoR SYSTEM ARE sM 2 TOTAL FoRCE 丹 CTING ON THE SySTEM CAN SIMA凵FBYN6TNGT以AT M C D UE CAN TREAT THE MASS CENTER SEPARATE USING THE EXTERWAL FORCEs AND THEN EXPREss THE MOT(ON OF EACH PARTICLE URT THE ADs ANT POIN TN THIS LECTOKE
5-8 FOR THE TORQUES, FIRST NOTE THAT SINCE Z M: X G工 zM;「;其 USE m;「; +2 +∑ BUT WE KNOW TH∑2x f THEREFORE WE ARE LEFT WITH z六x;A TOTAL TORQVE oA THE SY STEM ABOUT O 升GAA. NO SURPRISEs. CONVERT To WoRKING A BOUT C,M M:x 2M::/F +(已+成(了+( SIMPLI FIES SINCE 2 TERMS VAN(SH
59 DEFINE STEM ANGULAR MOM. ABOUT THE COM THEN i 了 YSTEM ANGVLAR MOM. OFC.0.M A BoUT O 1 ARE TIME0ERw所vE: h=kc+M「c又 BUT mre =F 户×主 ALREA0y5T升TE0T升T 2「: 5 X Fi COMPARE THESE 2 FINAL EQUATIONS:(*)AND * AND M RBOVT O WRT A BUT C0A.URT工小ERT吼 小 ERTIAL CONSTAANT IF M
