Download Circular motion - Leaving Cert Physics

Page 1 of 2
Circular motion
Angle in radians
=

arc length
radius
Convert degrees to radians
180
Linear velocity
Velocity =
r
s
r
 radians
=
Angular velocity
displacement
time
angular velocity =

v = s
t
=
=
=
angle traced out
time

t
Relationship between linear velocity and angular velocity
 =
v
v = r 
Proof : linear velocity = radius x angular velocity
(v = r)
Suppose the moving particle traces out an angle  in time t seconds as it moves a
distance s
From the definition of the radian

t
=
s
rt

 =
t
 =
 =
r = v
 = s
r
s x 1
t
r
v x 1
r
v
r
divide both sides by t
but  =  / t
v = s/t
Page 2 of 2
Note : A body travelling in a circular path with a constant speed has a
changing velocity (due to the change in direction) and is
therefore accelerating
Centripetal acceleration: the acceleration towards the centre of a circle
of a body moving in a circular path.
Linear centripetal acceleration
a
=
v2
r
Angular centripetal accelaration
a = r 2
(page 40 tables)
Centripetal force : the force towards the centre needed to keep a body
moving in a circular path.
Note Force = mass x acceleration
Linear centripetal force
F = m v2
r
F =
mxa
Angular centripetal force
F
=
m r 2