CIRCULAR MOTION

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


= angular displacement
=s/r
1 revolution: = 2r/r = 2 rad = 360° => 1 rad 57.3°

: v. small angle => s considered st. line perpendicular to radius at start
sin = s/r = => for v.small angles: sin =

Angular velocity, (rad/s or s^-1): rate of change of angular displacement (angle turned per unit time)
const speed:
  =
     t
varying speed: = d/dt

Frequency, f (hertz, Hz): rate of rotation
f= # of rotations/time

Period, T (s): time for 1 revolution
T = f^-1

for 1 revolution: = /t = 2/T = 2f


const speed: v = s/t [v= linear vel]
= t = s/r => s = tr
v = tr/t = r
linear vel = angular vel x radius: const speed
v = r

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 = ²r
F = ma => F = mv²/r = m²r


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