1. Circular / rotational motion

2. You figure it out… Do the ‘spinning disk’ activity
What’s the difference between
Linear speed/ velocity?
Angular/rotational speed/velocity?
Do the ‘quarter and coin’ activity
Rotation and
Revolution?

3. Rotation is…. Circular motion around an object’s internal axis
Around a point inside the object
Example:
Earth on its own axis
CD, DVD, record
Ice skater in a spin

4. Revolution is… Circular motion around an external axis Examples:
a point outside of the object
Examples:
earth around the sun (ok it’s elliptical)
Child on a merry-go-round

5. What about different points on the same rotating object?
Every point on the object undergoes circular motion about the point O
All parts of the object of the body rotate through the same angle during the same time
The object is considered to be a rigid body
This means that each part of the body is fixed in position relative to all other parts of the body
REMEMBER THE DOTS ON THE LAZY SUSAN DISK?
Like kids on a merry-go-round!

6. Describing circular motion
Linear speed/velocity - the (arc length) distance moved per unit time.
Angular/rotational speed/velocity - the number of degree, radians, or revolutions per unit time.
How can we measure the above for a spinning disk?

7. Angular speed in revolutions/sec
Easy!
Start timer
Count a predetermined # of complete revolutions
Stop timer
Divide # rev/ measured time
Angular speed in rev/sec is the reciprocal of the period T

8. T = 1 / f f = 1 / T Period and Frequency
The Period (T) of a body travelling in a circle at constant speed is time taken to complete one revolution - measured in seconds
Frequency (f) is the number of revolutions per second – measured in Hz
In circular motion aka angular/rotational speed
T = 1 / f f = 1 / T

9. How to calculate linear speed?
Identify the radial position, r = ??
Calculate the circumference of the circular path
2πr
Multiply (2πr) x (#rev) to get total distance
Divide by total time
Another way
Linear speed v = 2πr / T = circumference / period

10. Various Units for displacement and angular speed
Degrees, radians, revs / sec
1 radian =~ 57º
2π = 6.28 radians in a whole circle
360 degrees = 2π radians = 1 circumference or rev. =
2πr in linear distance

11. If Angular speed is in radians/sec…
Angular speed ω is the angle turned through per second
ω = θ/t = 2π / T
2π = whole circle angle
T = time to complete one revolution
So what’s the mathematical relationship between linear and angular speed?

12. Relationship Between Angular and Linear Quantities
Displacements
Speeds
Every point on the rotating object has the same angular motion
Every point on the rotating object does not have the same linear motion

13. Example
On a merry-go-round the horses on the outer rail are located 2 times as far from the horses on the inside rail. If a girl sits on a horse on the inside rail at a rotational speed of 3 RPM and a linear speed of 2 m/s, what will be the rotational speed and linear speed of her brother who is on a horse on the outer rail?
His rotational speed: the same at 3 RPM.
His linear speed: 2 times faster or 2 x 2 = 4 m/s.

14. Practice problem solving
Circular motion worksheet
Our first problems will deal with describing motion
Objects that are rotating
Objects that are sitting on /attached to rotating objects
Next topic: why do objects move in circular motion?
Think Newton’s laws…..