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formula sheet dynamics, Exercises of Dynamics

Dynamics formula sheet test 1

Typology: Exercises

2016/2017

Uploaded on 10/26/2017

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MAE/CE 272 Midterm Exam 1 Formula Sheet
Notations: Vector parameters are typed in boldface. Scalar parameters are typed in italics.
Chapter 12: Kinematics of particles
Rectilinear motion: dx =v dt;dv =a dt;a dx =v dv
Curvilinear motion: dr=vdt;dv=adt
Rectangular coordinates: v= ˙xˆ
i+ ˙yˆ
j+ ˙zˆ
k
a= ¨xi+ ¨yj+ ¨zk
Tangential-normal coordinates: v=vˆ
ut
a=dv
dt ˆ
ut+v2
ρˆ
un
Radial-transverse (polar) coordinates: v= ˙rˆ
ur+r˙
θˆ
uθ
a= rr˙
θ2)ˆ
ur+ (r¨
θ+ 2 ˙r˙
θ)ˆ
uθ
Chapter 16: Kinematics of rigid bodies
Translation: dx =v dt;dv =a dt;a dx =v dv
Rotation: =ω dt; =α dt;α =ω
Two points on the same body: vB=vA+ω×rB/A
aB=aA+α×rB/A ω2rB/A
Two points on separate bodies: vB=vA+×rB/A + (vB/A)xyz
(i.e. rotating axes) aB=aA+˙
×rB/A 2rB/A + 2×(vB/A)xyz + (aB/A)xy z

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MAE/CE 272 Midterm Exam 1 Formula Sheet

Notations: Vector parameters are typed in boldface. Scalar parameters are typed in italics.

Chapter 12: Kinematics of particles

Rectilinear motion: dx = v dt; dv = a dt; a dx = v dv

Curvilinear motion: dr = vdt; dv = adt

Rectangular coordinates: v = ˙x

i + ˙y

j + ˙z

k

a = ¨xi + ¨yj + ¨zk

Tangential-normal coordinates: v = vˆu t

a =

dv

dt

uˆ t

v

2

ρ

uˆ n

Radial-transverse (polar) coordinates: v = ˙ruˆ r

  • r

θuˆ θ

a = (¨r − r

θ

2 )ˆu r

  • (r

θ + 2 ˙r

θ)ˆu θ

Chapter 16: Kinematics of rigid bodies

Translation: dx = v dt; dv = a dt; a dx = v dv

Rotation: dθ = ω dt; dω = α dt; α dθ = ω dω

Two points on the same body: v B

= v A

  • ω × r B/A

aB = aA + α × r B/A

− ω

2

r B/A

Two points on separate bodies: vB = vA + Ω × r B/A

  • (v B/A

)xyz

(i.e. rotating axes) a B

= a A

Ω × r B/A

2 r B/A

  • 2Ω × (v B/A

xyz

  • (a B/A

xyz