21-23. Show that if the angular momentum of a body is determined with respect to an arbitrary point A, then H can be expressed by Eq. 21-9. This requires substituting PA = PG + PG/A into Eq. 21-6 and expanding, noting that PG dm 0 by definition of the mass center and = VG = V₁ + @ X PG/ A- X Z Z PG|A G Prob. 21-23 PG P PA Y
21-23. Show that if the angular momentum of a body is determined with respect to an arbitrary point A, then H can be expressed by Eq. 21-9. This requires substituting PA = PG + PG/A into Eq. 21-6 and expanding, noting that PG dm 0 by definition of the mass center and = VG = V₁ + @ X PG/ A- X Z Z PG|A G Prob. 21-23 PG P PA Y
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In this problem after expanding, I am wondering how I can cancel two final terms in my handwriting work, because if I group (rho_G . dm) into the integral and leave (rho_G/A x omega) outside the integral it will be conflicting. I said that because I also see in the H_G formula, if we can do the same thing (group (rho_G . dm)) it will make H_G become zero too. So please explain and show me how to solve this problem. Thank you.
Transcribed Image Text:21-23. Show that if the angular momentum of a body is
determined with respect to an arbitrary point A, then H
can be expressed by Eq. 21-9. This requires substituting
PA = PG + PG/A into Eq. 21-6 and expanding, noting
that PG dm 0 by definition of the mass center and
=
VG = V₁ + @ X PG/ A-
X
Z
Z
PG|A
G
Prob. 21-23
PG P
PA
Y
![21-23
H₁ = ([ PA.dm ) X UA + SPA x (w x Pp) dm
A
PA = PG + PG/A
=) =
~)HA- ( f (PG+ fam) dm) x + (
v
Å
я
m
+
Stea
+ SG/A) x ( w x . ( PG + f G/A ]]dm}
O
(Pacha xus+ (pap dala
XUA
t
+ SP₁ x (wxfa) dm + SPAX (wxla/).dm
G/A
Adn
‡
SP GIA X (wx faldm + SPX ( w x Pap
Gr](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F95e46d76-a2ab-48ca-a2a4-77f788bd73e0%2F2b58540f-44cd-4edd-aaf6-082ed59b863d%2F0v5k2n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:21-23
H₁ = ([ PA.dm ) X UA + SPA x (w x Pp) dm
A
PA = PG + PG/A
=) =
~)HA- ( f (PG+ fam) dm) x + (
v
Å
я
m
+
Stea
+ SG/A) x ( w x . ( PG + f G/A ]]dm}
O
(Pacha xus+ (pap dala
XUA
t
+ SP₁ x (wxfa) dm + SPAX (wxla/).dm
G/A
Adn
‡
SP GIA X (wx faldm + SPX ( w x Pap
Gr
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