1. Circular Motion Unit 5 http://www.youtube.com/watch?v=-G7tjiMNVlc

2. What is “circular motion”?
An object that moves in a circular path about an external point is in circular motion.

3. Rotation v. Revolution
Rotation – When an object turns about an internal axis.
Ex. Earth rotates on an axis passing through it’s geographical poles every 24 hrs.
Revolution – When an object turns on an external axis.
Ex. Earth revolves around the sun every days.

4. Period vs. Frequency
Period ( T ) – time it takes for one full rotation or revolution
Measured in seconds
Frequency ( f ) – number of rotations in one sec
Measured in Hertz (Hz)
Which is an inverse sec

5. Example 1

6. Arc Length
Refers to the length, in meters, that an object travels along the circumference of a circle.
The symbol for arc length is s s

7. Angle Arc length depends on the radius.
Any point on the radius will have the same angular displacement.
Angle in this case is measured in radians and NOT degrees. s r θ

8. Angular vs. Linear Velocity
Angular velocity (w)
Speed object travels while in circular motion
Does NOT depend on radius
Units
rotations/sec OR revolutions/sec
Tangential (linear) velocity
Speed object travels when released from circle
Travels in a straight path tangent to the circle
Depends on length of radius
m/s

9. The Value of VT
The tangential speed depends on the size of the path’s radius.
As radius decreases, vT increases

10. Example 2

11. The Change in vT Velocity Speed – constant in circular path
Direction-changes direction
So…..velocity changes which is the definition of acceleration
Acceleration
Centripetal acceleration (ac)
Direction of ac is towards the center

12. Example 3

13. Centripetal Force
For circular motion, the net force influencing acceleration is called a centripetal force.
Force that keeps an object going in a circular path.
This force is directed toward the center of rotation or center of a curvature.

14. Centripetal Force
If there was no centripetal force, what would be the direction of the occupants of a merry-go-round?
They would continue on a straight line due to the object’s inertia and maintain their instantaneous tangential velocity.

15. Ball on a String Example
Inertia maintains ball’s motion in a linear path
Tension on the string is an applied net external force directed toward the center of rotation
Causes a constant change in velocity, making the ball follow a circular path

16. Centripetal Force
Using Newton’s Second Law equation (Fnet = ma),

17. Example 4