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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 = ẋ̂i + ẏĵ+ żk̂ a = ẍi+ ÿj+ z̈k

Tangential-normal coordinates: v = vût a = dv

dt ût +

v2

ρ ûn

Radial-transverse (polar) coordinates: v = ṙûr + rθ̇ûθ a = (r̈ − rθ̇2)ûr + (rθ̈ + 2ṙθ̇)ûθ

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: vB = vA + ω × rB/A aB = aA +α× rB/A − ω

2rB/A

Two points on separate bodies: vB = vA +Ω× rB/A + (vB/A)xyz (i.e. rotating axes) aB = aA + Ω̇× rB/A − Ω

2rB/A + 2Ω× (vB/A)xyz + (aB/A)xyz