CIRCULAR MOTION
MEASURING CIRCULAR
MOTION (METHOD 1)
1
complete rotation =
1 revolution
 Measure rotational
motion by counting
the number of
rotations
 Most common unit of
measurement =
revolution
(abbreviated rev)
MEASURING CIRCULAR
MOTION (METHOD 2)
360°
 Can
also measure using degrees
 1 rotation = 1 revolution = 360°
MEASURING CIRCULAR
MOTION (METHOD 3)
Θ=s/r
 Radian
(rad): angle
with vertex at center
of circle whose sides
cut off an arc on
circle equal to its
radius
 Radius = r
 Length of arc = s
 angle = 1 radian
 Unitless dimension –
use rad to avoid
confusion
CONVERTING BETWEEN DIFFERENT
MEASUREMENT
By definition: 1 rev = 360° = 2π rad
 Convert 10π rad to revolutions

CONVERTING FROM DEGREE TO RAD
θrad=(π/180)θdegrees
Convert 75 degrees to radians
ANGULAR DISPLACEMENT
Distance through which any point on rotating
body moves (angular distance instead of linear
distance)
 Example: when a wheel makes one complete
rotation, it’s angular displacement has been 1
rev, 2π rad, or 360°

ANGULAR VELOCITY
 Similar
to linear velocity, except instead of
linear displacement, use angular displacement
 Angular velocity = rev/time
 OR ω = angular displacement (θ)/time (t)
 Units = rad/s or rev/min
ω=
θ
t
EXAMPLE

A motorcycle wheel turns 7200 times while being
ridden for 10 min. What is the angular velocity in
rev/min?
LINEAR VELOCITY
 The
linear speed on
any point on rotating
circle = v = ωr
v = linear velocity
ω = angular velocity
r = radius
 Can
measure using
stroboscope or strobe
light
EXAMPLE: LINEAR VELOCITY
A wheel of 1.00 m radius turns at 1000 rpm. Find the
linear speed of a point on the rim of the wheel.
ANGULAR ACCELERATION
Angular acceleration = rate of change of angular velocity
α=
Δω
t
α = angular
acceleration
Δω = change in angular
velocity
t
= time
EQUATIONS: LINEAR VS. ROTATIONAL
MOTION
Linear Motion Equations
s = vavgt
Rotational Motion
Equations
θ = ωavgt
s = vit + ½aavgt2
θ = ωit + ½αavg t2
vavg = (vf + vi)/t
ωavg = (ωf + ωi)/t
aavg = (vf – vi)/t
αavg = (ωf – ωi)/t
2aavgs = vf2 – vi2
2αavgθ = ωf2 – ωi2
SAMPLE CALCULATIONS
To calculate various components of angular
motion, click on the link listed below:
http://canario.iqm.unicamp.br/MATDID/HyperPhys
ics/hbase/rotq.html
