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
why is object in circular motion move with constant speed
centripetal force is perpecdicular to velocity so no component in direction of motion, no work done on object so constant speed
define centripetal force
net force that acts perpendicular to the direction of velocity - towards centre of circle
define angular velocity
rate of change of angle
