Formula_Sheet_HW7

# Formula_Sheet_HW7 - ο£ β r r& r r = i i m r m β r i...

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v = ds dt a = dv dt = 2 2 d s dt v dv = a ds v r = dr dt r a r = dv dt r = 2 2 d r dt r v = v 0 + a c t s = s 0 + v 0 t + 1 2 a c t 2 v 2 = v 0 2 + 2a c (s – s 0 ) v r = v t e r ; v = ρ β a r = a t t e r + a n n e r a t = v = s a n = v β = ρ β 2 = 2 v ρ t e r = β n e r 3 2 2 2 2 dy 1 dx d y dx + ρ = r r = r r e r v r = r r e r + r θ e θ r a r = ( r && - r θ 2 ) r e r + ( r θ + 2 r θ ) e θ r r e r = θ e θ r e θ r = - θ r e r v r = ( R ) R e r + ( R θ cos φ ) e θ r + ( R φ ) e φ r a r = ( R && - R φ 2 - R θ 2 cos 2 φ ) R e r + ( cos R φ d dt (R 2 θ ) – 2R θ φ sin φ ) e θ r + ( 1 R d dt (R 2 φ ) + R θ 2 sin φ cos φ ) e φ r f μ N dU = F r d r r P = F r v r F r = m a r ' 1 2 U - = Δ T + Δ V g + Δ V e T = 1 2 mv 2 ; V g = mgh ; V e = 1 2 kx 2 ( ) 2 1 t t t t F dt = = r = 2 G r - 1 G r G r = m v r ( ) 2 1 t t O t t M dt = = r = 2 O H r - 1 O H r O H r = r r × G r A v r = B v r + ω r × A/ B r r A a r = B a r + ω r × ( ω r × A/ B r r ) + α r × A/ B r r XY dV dt r = xy dV dt r + ω r × V r A v r = P v r + rel v r A a r = P a r + 2 ω r × rel v r + rel a r xy dV dt r = V x i r + V y j r T = 2 1 m v 2 + i 2 i m /G 1 m r 2 r G r = m v r G H r = i i m /G i m /G r m r × r r P H r = G H r + G /P r r × m v r ( ) P rel H r = i i m / P i m / P r m r ×

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Unformatted text preview: ο£» β r r & r r = i i m r m β r i F β r = m a r i F β r = G r & O M β r = O H r & G M β r = G H r & P M β r = G H r & + G /P r r Γ m G a r P M β r = ( ) P rel H r & + G /P r r Γ m P a r F β r = m a r M β r = I Ξ± r O M β r = I O Ξ± r P M β r = I G Ξ± r + G /P r r Γ m G a r P M β r = I P Ξ± r + G /P r r Γ m P a r U = M d ΞΈ β« P = M Ο T = 1 2 m 2 v + 1 2 I 2 Ο T = 1 2 I O 2 Ο T = 1 2 I C 2 Ο G r = m v r H r = I Ο r H r O = I O Ο r H P = I Ο + (m v ) d Slender Rod β I = 1 12 m l 2 Disk β I = 1 2 mr 2 I = I + md 2...
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## This document was uploaded on 02/17/2011.

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Formula_Sheet_HW7 - ο£ β r r& r r = i i m r m β r i...

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