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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.

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
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
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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