16 - Circular Motion Flashcards
explain how an object moving with circular motion at a constant speed has an acceleration
direction of the velocity is constantly changing, change in velocity means it is accelerating
uniform circular motion: v =
v=2πr/T or v=2πrf
define angular displacement
angle swept out at centre of circular path
angular velocity equation, units
ω=θ/t
measured in rads^-1
radian defined as…
angle swept out when s = r (arc radius)
s=θr
other units for angular speed
revolutions per second (revs^-1) or revolutions per minute (r.p.m.)
angular frequency
is the same as angular speed
ω=2π/T or ω=2πf
relationship between angular and linear speed
ω=2π/T > T=2π/ω
v=2πr/T
sub T from 1st > v=rω
linear speed = radius x angular speed
in what direction is centripetal force
towards centre
in what direction is the acceleration
towards centre, perpendicular to velocity direction
acceleration equation derivation
a=v^2/r and v=rw
so a=r2w2/r
a=rw^2
v=rw
so a=vw
circular motion occurs due to
force acting perpendicular to direction of motion (towards centre) causing an acceleration is that perpendicular direction also
equations for centripetal force
F=ma (subbing a=v^2/r or a=rw^2 or a=vw)
F=mv^2/r
F=mrw^2
F=mvw
force effect perpendicular direction of centre
weight is perpendicular to direction of centre so no effect on centripetal force
centripetal force is a combo of
vector sum of tension and weight
