CIRCULAR MOTION

1 radian = 1 rad = 1C = angle when arc = radius
radian: dimensionless

q = angular displacement
q =s/r
1 revolution: q = 2pr/r = 2p rad = 360° => 1 rad » 57.3°

dq: v. small angle => ds considered st. line perpendicular to radius at start
sin dq = ds/r = dq => for v.small angles: sin dq = dq
Angular velocity, w (rad/s or s-1): rate of change of angular displacement (angle turned per unit time)
const speed:
w = q
t
varying speed: w = dq/dt
Frequency, ¦ (hertz, Hz): rate of rotation
¦ = # of rotations/time
Period, T (s): time for 1 revolution
T = ¦ -1
for 1 revolution: w = q/t = 2p/T = 2pf

const speed: v = s/t [v= linear vel]
q = wt = s/r => s = wtr
v = wtr/t = wr
linear vel = angular vel x radius: const speed
v = wr
Centripetal acceleration: movement in a circle w/ uniform speed but changing vel, due to centripetal F acting towards centre of circle (F moves obj in circle, since F perpendicular to vel => doesn't change speed, only dirn)
const speed: a = v2/r = w2r
F = ma => F = mv2/r = mw2r
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