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= (¨r−r˙
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: 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 −ω2rB/A
Two points on separate bodies: vB=vA+Ω×rB/A + (vB/A)xyz
(i.e. rotating axes) aB=aA+˙
Ω×rB/A −Ω2rB/A + 2Ω×(vB/A)xyz + (aB/A)xy z