Rotational Kinematics

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Rotational Kinematics

let’s rap

discussion

Translational and rotational quantities compared
concepttranslationconnectionrotation
base quantitiess, r s = θ × rθ 
coordinate systems r =  x î + y ĵx = 
y = 
r2 = 
θ = 
r cos θ
r sin θ
x2 + y2
tan−1 (y/x)
r =  r r̂ + θ θ̂
velocityv = dr/dtv = ω × rω = dθ/dt
accelerationa = dv/dt = d2r/dt2a = α × r − ω2rα = dω/dt = d2θ/dt2
equations of motionv = 
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: 1⅝ ips
      • 8-track: ??
      • open reel (reel-to-reel): 15 ips, 7½ips
    • data tape
      • 9-track: ??
    • videotape
      • VHS: ??
      • Betamax: ??
      • open reel (reel-to-reel): ??
    • optical disk
      • laserdisc, extended play: 18.96 m/s
      • CD: 1.2–1.4 m/s
      • DVD:
        • 3.49 m/s (single layer)
        • 3.84 m/s (double layer)
  • constant angular velocity
    • phonograph, cylinder
      • 160 rpm
    • phonograph, disk
      • 78.26 rpm
      • 45 rpm
      • 33⅓ rpm
      • 16⅔ rpm
    • video
      • laserdisc, standard play: 1800/1500 rpm
    • magnetic data storage
      • floppy disk: ??
      • hard drive: ??
Selected angular speeds* period of rotation, rpm revolutions per minute, Hz = hertz = revolutions per second

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