Rotational Kinematics

Discussion

let's rap

discussion

Translational and Rotational Quantities Compared
  translational connections rotational
base quantities s, r   s =  θ × r θ  
coordinate systems
 r = 
x î + y ĵ

 x = 
y = 
r2 = 
θ = 		 r cos θ
r sin θ
x2 + y2
tan−1 (y/x)
 r = 
rr̂ + θθ̂
velocity v =  dr/dt v =  ω × r ω =  dθ/dt
acceleration  a =  dv/dt = d2r/dt2  a =  α × r − ω2r  α =  dω/dt = d2θ/dt2
equations of motion v = 
x = 
v2 = 		 v0 + at
x0 + v0t + ½at2
v02 + 2a(x − x0)		     ω = 
θ = 
ω2 = 		 ω0 + αt
θ0 + ω0t + ½αt2
ω02 + 2α(θ − θ0)

the museum of obsolete technology

  • constant linear velocity
    • movie film
      • 24 fps
    • audio tape
      • cassette: 15/8 ips
      • 8-track: ??
      • open reel (reel-to-reel): ??
    • data tape
      • 9-track: ??
    • videotape
      • VHS: ??
      • Betamax: ??
      • open reel (reel-to-reel): ??
    • optical disk
      • CD: 1.2–1.4 m/s
      • DVD:
        • 3.49 m/s (single layer)
        • 3.84 m/s (double layer)
  • constant angular velocity
    • phonograph
      • Edison cylinder
      • 78 rpm
      • 45 rpm
      • 33 1/3 rpm
      • 16 2/3 rpm
    • video
      • laser disc: 11 m/s
    • magnetic data storage
      • floppy disk: ??
      • hard drive: ??
      • Zip disk: ??
      • Jaz disk: ??

The Physics Hypertextbook

  • No condition is permanent.