1. Rotational Motion and the Law of Gravity
Measuring Rotational Motion

2. Rotational Quantities
Rotational motion – the motion of an object that spins about an axis
When an object spins
Axis of rotation – the line about which the rotation occurs
Circular motion – when an object spins around a single axis
Arc length – the distance an object moves around the circumference of the circle

3. Rotational Quantities
Radian – an angle whose arc length is equal to its radius, which is approximately equal to 57.3o
Angular displacement – how much an object has rotated
Measured in radians (rad)

4. Rotational Quantities
Angular displacement (in radians) = the change in arc length/the length of the radius
Δθ=Δs/r
Δθ is positive for counterclockwise rotation and negative for clockwise rotation

5. Rotational Quantities

6. Rotational Quantities
Angular speed – rate of rotation
Measured in radians per second (rad/s)
Sometimes measured in revolutions per unit of time, such as seconds (rev/s) or minutes (rev/min or RPM’s)
Represented by the lowercase Greek letter omega (ω)
Some times called average angular speed (ωavg)
Average angular speed = angular displacement/time interval
ωavg= Δθ/Δt

7. Rotational Quantities
Angular acceleration occurs when angular speed changes
Measured in radians per second2 (rad/s2)
Represented by the lowercase Greek letter alpha (α)
Average angular acceleration = change in angular speed/time interval
αavg = (ω2- ω1)/(t2-t1) = Δω/Δt
All points on a rotating rigid object have the same angular acceleration and angular speed

8. Comparing Angular and Linear Quantities
Every angular quantity matches up with a corresponding linear quantity
θ matches up with x
ω matches up with v
α matches up with a
We have a series of equations for rotational motion with constant angular acceleration

9. Comparing Angular and Linear Quantities