1. Circular motion

2. 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)

3. Measuring Circular Motion (Method 2)
360°
Can also measure using degrees
1 rotation = 1 revolution = 360°

4. 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

5. Converting between different measurement
By definition: 1 rev = 360° = 2π rad
Convert 10π rad to revolutions

6. Converting from Degree to Rad
θrad=(π/180)θdegrees
Convert 75 degrees to radians

7. 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°

8. 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 θ t
ω =

9. Example
A motorcycle wheel turns 7200 times while being ridden for 10 min. What is the angular velocity in rev/min?

10. 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

11. 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.

12. α = Δω t Angular Acceleration α = angular acceleration
Angular acceleration = rate of change of angular velocity
α = angular acceleration
Δω = change in angular velocity
t = time Δω t
α =

13. Equations: Linear vs. Rotational Motion
Linear Motion Equations
Rotational Motion Equations
s = vavgt
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

14. Sample Calculations
To calculate various components of angular motion, click on the link listed below:
ics/hbase/rotq.html