The Physics
Opus in profectus

Rotational Kinematics

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Translational and rotational quantities compared
concept translation connection rotation
base quantities s, r s =  θ × r θ
coordinate systems
r = 

x  + y 

x = 
y = 
r2 = 
θ = 
r cos θ
r sin θ
x2 + y2
tan−1 (y/x)

r = 

r  + θ θ̂

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

Selected angular speeds * period of rotation, rpm revolutions per minute, Hz = hertz = revolutions per second
device, event, phenomenon, process frequency ω (rad/s)
planet Venus, the slowest planet (and backward)−5,832.5hour*2.99 × 10−7
planet Earth, the just right planet23.9345hour*7.29 × 10−5
great red spot of Jupiter 10−4 Hz 10−5
analog clock, hour hand12hour*0.000145
planet Jupiter, the fastest planet9.9250hour*0.000176
analog clock, minute hand1hour*0.00175
London eye30min*0.00349
analog clock, second hand1min*0.105
tornado core 0.1 Hz 6
phonograph record, long play (LP)33⅓rpm3.49
phonograph record, extended play (EP)45rpm4.71
phonograph record, disk (1925 standard)78.26rpm8.20
phonograph record, cylinder (1902 standard)160rpm16.8
laserdisc, standard play, PAL/SECAM1,500rpm157
laserdisc, standard play, NTSC1,800rpm188
hard drive, standard (1990~2000)3,600rpm377
hard drive, laptop (ca. 2010)4,500rpm471
hard drive, economy (ca. 2010)5,400rpm565
hard drive, standard (ca. 2010)7,200rpm754
hard drive, premium (ca. 2010)15,000rpm1,570
pulsar, fastest known (PSR J1748–2446ad)716Hz4,500
microgyroscope (fastest "man-made" rotation) 107Hz 108
quark-gluon plasma (fastest rotating fluid) 1020 Hz 1021
Planck angular frequency (absolute limit)√(c5/ℏG)1.86 × 1043