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Equation Sheet - Final Exam, Study notes of Dynamics

University of Diyala (UD)Dynamics

ME 274: Basic Mechanics II. Fall 2016. December 12, 2016. Final Exam: Equation Sheet. vP = ˙xî+ ˙yj. = vP êt. = ˙rêr + r. ˙ θêθ. aP = xî+ ÿj. = ˙vP êt +.

Typology: Study notes

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ME 274: Basic Mechanics II
Fall 2016
December 12, 2016
Final Exam: Equation Sheet
~vP= ˙xˆ
i+ ˙yˆ
j
=vPˆet
= ˙rˆer+r˙
θˆeθ
~aP= ¨xˆ
i+ ¨yˆ
j
= ˙vPˆet+v2
P
ρˆen
= (¨r−r˙
θ2)ˆer+ (r¨
θ+ 2 ˙r˙
θ)ˆeθ
~vB=~vA+~ω ×~rB /A
~aB=~aA+~α ×~rB /A +~ω ×~ω ×~rB/A
~vB=~vA+ (~vB /A)rel +~ω ×~rB/A
~aB=~aA+ (~aB/A)rel +~α ×~rB/A + 2~ω ×(~vB/A)rel +~ω ×~ω ×~rB/A
~
F=m~aG
~
MA=IA~α +~rG/A ×m~aA
T1+V1+Unc
1→2=T2+V2T=1
2mv2
A+1
2IAω2+m~vA•(~ω ×~rG/A)
m~vG1+Zt2
t1X~
F dt =m~vG2
~
HO1+Zt2
t1X~
MOdt =~
HO2
~
HA1+Zt2
t1X~
MAdt =~
HA2
~
HO=~rP/O ×m~vPor ~
HA=IA~ω
e=−vBn2−vAn2
vBn1−vAn1
IG,disk =1
2mr2IG,bar =1
12mL2
M¨x+C˙x+Kx =F(t)ωn=rK
M2ζωn=C
M
xP(t) = Acos ωt +Bsin ωt
Final Exam: Equation Sheet Page 1 of 1

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ME 274: Basic Mechanics II

Fall 2016

December 12, 2016

Final Exam: Equation Sheet

~v P

= ˙x

i + ˙y

j

= vP ˆet

= ˙rˆer + r

θeˆ θ

~a P

= ¨x

i + ¨y

j

= ˙v P

eˆ t

v

2

P

ρ

ˆe n

= (¨r − r

θ

2

)ˆer + (r

θ + 2 ˙r

θ)ˆeθ

~v B

= ~v A

  • ~ω × ~r B/A

~aB = ~aA + ~α × ~r B/A

  • ~ω ×

~ω × ~r B/A

~v B

= ~v A

  • (~v B/A

rel

  • ~ω × ~r B/A

~aB = ~aA + (~a B/A

)rel + ~α × ~r B/A

  • 2~ω × (~v B/A

)rel + ~ω ×

~ω × ~r B/A

F = m~aG

M

A

= I

A

~α + ~r G/A

× m~a A

T 1 + V 1 + U

nc

1 → 2

= T 2 + V 2

T =

mv

2

A

I

A

ω

2

  • m~v A
  • (~ω × ~r G/A

m~vG 1 +

t 2

t 1

F dt = m~vG 2

HO 1 +

t 2

t 1

MOdt =

HO 2

H

A 1

t 2

t 1

M

A

dt =

H

A 2

H

O

= ~r P/O

× m~v P

or

H

A

= I

A

~ω

e = −

v Bn 2

− v An 2

v Bn 1

− v An 1

I

G,disk

mr

2 I G,bar

mL

2

M x¨ + C x˙ + Kx = F (t)

ωn =

K

M

2 ζω n

C

M

x P

(t) = A cos ωt + B sin ωt

Final Exam: Equation Sheet Page 1 of 1