Chpe 6 Pne oon of Rd ode 6. Equon of oon fo Rd bod. 6., 6., 6.3 Conde d bod ced upon b ee een foce,, 3,. We cn ume h he bod mde of e numbe n of pce of m Δm (,,, n). Conden f he moon of he m cene of he bod wh epec o he ewonn fme of efeence Oz, m whee m he m of he bod nd he cceeon of he m cene : he m cene of em of pce moe f he ene m of he em nd he een foce wee concened he pon. Tunn now o he moon of he bod ee o he cenod fme of efeence z, whch ne wh epec o he ewonn fme of efeence Oz, H H& ( m ) 6-
whee H he nu momenum bou of he em of pce fomn he d bod; he momen eun bou of he een foce equ o he e of chne of he nu momenum bou of he em of pce. 6.3 nu omenum of Rd od n Pne oon. 6.4 H H& ( Δ m ) ( ( ) Δm ) ( ) Δm I I& I whee I epeen he momen of ne of he b bou cenod pependcu o he b. 6.4 Pne oon Of Rd od. D embe Pncpe ue 6. Conde d b of m m mon unde he con of ee een foce,, 3, conned n he pne of he b. Wn he fundmen equon of moon n c fom, m m I D embe Pncpe The een foce cn on d bod e equen o he ece foce of he ou pce cn on d bod (. 6.6). 6-
Tnon (. 6.8) m m I Cenod Roon (. 6.9) m m I ene Pne oon (. 6.7) The moon of he b defned b he eun nd momen eun bou of he een foce cn on. The ene pne of he een foce cn on he bod doe no p houh he m cene of he bod. 6.6 Souon of Pobem non he oon of Rd od The eouon of he pne moon of d bod no non nd cenod oon bc concep whch cn be pped houhou he ud of mechnc. Th ppoch cn be eended o he ud of ene 3-D moon of d bod. Empe 6.) When he fowd peed of he uc w m/, he be wee udden pped, cun fou whee o op on. I w obeed h he uc dded o e n 6 m. Deemne he mnude of he nom econ nd of he fcon foce ech whee he uc dded o e. The uc h m of,..m.m.m 6-3
n) Un he equon of unfom cceeed moon, we we Knemc of oon W m ( 3)( 9.8m ) 9.43 f m S 8.33m f S 6m Knec of oon Thee equon of moon e obned b epen h he em of he een foce equen o he em of he ece foce. ( ) : ( ) : ( ) ( ) : m(.m) ( 3.6m) m(.m) 6.6 4.7 W m m m 8.33m 9.8m 7.6.849 7.37 Empe 6.) unfom phee of m m nd du pojeced on ouh hozon ufce wh ne eoc nd no nu eoc. Denon b he cocen of nec fcon beween he phee nd he foo, deemne () he me whch he phee w on whou dn, (b) he ne eoc nd nu eoc of he phee me. 6-4
6- n) Epen h he em of he een foce equen o he em of he ece foce, we we Equon of oon Knemc of oon on he phee boh oe nd de, ne nd nu moon e unfom cceeed. The phee w on whou dn when he eoc C of he pon of conc C zeo. h me,, pon C become he nnneou cene of oon, nd we he Homewo Pobem 6., 6.34, 6.3, 6.69 m m m I I m m m m m W W : : : () 7 7 7
6-6 6.8 Conned Pne oon o enneen ppcon de wh d bode whch e mon unde en conn. In uch ce, defne eon e beween he componen of he cceeon of he m cene of he bod condeed nd nu cceeon ; he coepondn moon d o be conned moon. Empe ) Suppoe h he ue of,, nd e nown en nn nd h we wh o deemne he coepondn ue of he foce P, we he econ nd. (. 6.) n) Recn he nemc eon n Secon.8, ppn D embe pncpe, we obn P, nd fom he equon: n n n n n n j j I P m P m W n
Empe ) Suppoe now h he pped foce P, he ne, nd he nu eoc of he od e nown en nn nd h we wh o fnd he nu cceeon of he od nd he componen nd of he cceeon of m cene h nn. n) Thee equon cn be deed n em of, nd : n n W m m n P m m n n P I Pcu Ce of conned Pne oon: - non of d bod: - cenod oon: - noncenod oon: - on moon: oncenod Roon:. 6.4 & 6. - The moon of d bod conned o oe bou fed whch doe no p houh m cene. The m cene of he bod moe on cce of du ceneed he pon O. - The cceeon of : n - Snce ne O beon o he bod, nu eoc nd nu cceeon o epeen 6-7
he nu eoc nd he nu cceeon of he bod n moon ee o. - ppn d embe pncpe(. 6.), ( m ) ( I m ) I I O O - The em of een foce no equen o coupe of momen I o ; On when he oon cenod, he em of ece foce educe o coupe when O concde wh. Ron oon:. 6.7 - umn h he d bnced, o h m cene nd eomec cene concde, 6-8
- The een foce e equen o he eco nd coupe hown n. 6.7. - Thee dffeen ce of on: Ron, no dn: Ron, dn mpendn: Ron nd dn: whee he fcon foce, c fcon cocen, nec fcon cocen. Homewo 6., 6.3, 6.38 6-9