The Physics
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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 (smallest to largest) *period of rotation, in terms of angular speed,
rpm = revolution per minute, Hz = hertz = revolution per second
frequency ω (rad/s) device, event, phenomenon, process
−5,832.5hour*2.99 × 10−7 planet Venus, the slowest planet (and backward)
4.0 day* 1.82 × 10−5 Great Red Spot of Jupiter
23.9345hour*7.29 × 10−5 planet Earth, the just right planet
12hour*0.000145 analog clock, hour hand; 2 rotations per day
9.9250hour*0.000176 planet Jupiter, the fastest planet
1hour*0.00175 analog clock, minute hand; 1 rotation per hour
30min*0.00349 London eye
1min*0.105 analog clock, second hand; 1 rotation per minute
0.1 Hz 0.6 tornado core
    1 1 radian per second, the SI unit of angular speed
33⅓rpm3.49 phonograph record, long play (LP)
45rpm4.71 phonograph record, extended play (EP)
60 rpm 6.283 1 rotation per second
78.26rpm8.20 phonograph record, disk (1925 standard)
160rpm16.8 phonograph record, cylinder (1902 standard)
1,500rpm157 laserdisc, standard play, PAL/SECAM
1,800rpm188 laserdisc, standard play, NTSC
3,600rpm377 hard drive, standard (1990~2000)
4,500rpm471 hard drive, laptop (ca. 2010)
5,400rpm565 hard drive, economy (ca. 2010)
7,200rpm754 hard drive, standard (ca. 2010)
15,000rpm 1570 hard drive, premium (ca. 2010)
716Hz 4500 fastest astronomical object (pulsar J1748–2446ad)
107Hz 108 fastest human-made object (microgyroscope)
1020 Hz 1021 fastest fluid (quark-gluon plasma)
√(c5/ℏG)1.86 × 1043 theoretical limit (Planck angular frequency)