1. Chapter 9
Circular Motion

2. The time it takes for 1 full rotation of an object.
How long???
Period
The time it takes for 1 full rotation of an object.
T = 1/ƒ
Period = 1/frequency
s = 1/Hz

3. The number of rotations per unit of time.
How many??
Frequency
The number of rotations per unit of time.
Measured in Hz. (Hertz)

4. Linear (Tangential) Speed
When an object spins in a circle…
distance = circumference
vc = 2πr T
Linear speed = 2π * radius
Period
m/s = m s

5. Please note…
An object can move around a circle with a CONSTANT SPEED, yet still be accelerating!
How?????????
Because its direction is
always changing!

6. Centripetal Acceleration
Always directed toward the center of the circle.
ac = v2 r
Centripetal acc = (linear speed)2
radius
m/s2 = m/s m

7. Centripetal Force Fc = mac
Always directed toward the center of the circle.
Fc = mac
Centripetal force = mass * centripetal acc.
N = kg * m/s2

8. Example 1
After closing a deal with a client, Kent leans back in his swivel chair and spins around with a frequency of 0.5 Hz. What is Kent’s period of spin?
T = 1/ƒ
2 s

9. Example 2
Curtis’ favorite disco record has a scratch 0.12 m from the center that makes the record skip 45 times each minute. What is the linear speed of the scratch as it turns?
1st find the period: T = 1/f
T = 1.3 s
2nd find the linear speed: v = 2πr/T
V = .58 m/s

10. Example 3
Missy’s favorite ride at the fair is the rotor, which has a radius of 4.0 m. The ride takes 2.0 s to make one full revolution.
What is Missy’s linear speed?
v = 2πr/T
v = 13 m/s
What is Missy’s centripetal acceleration?
ac = v2/r
ac = 42 m/s2

11. Example 4
Captain Chip pilots a 60,500 kg plane. He must circle above the airport to wait his turn to land. If Chip flies his plane in a circle whose radius is 50,000. m every 1,800. s, what centripetal force must the air exert against the wings to keep the plane moving in a circle?
First, find the speed: v = 2πr/T
v = m/s
Next find centripetal force: Fc = mv2/r
Fc = 37,100 N

12. Abby 

13. Which trajectory does the ball follow?
A ball on a string is swung in a circle. The string breaks.
Which trajectory does the ball follow? A? B? C? D?
STT7.5
C. The line that is tangent!!

14. path of ball if the string
Ball on a string
The tension in the string
provides the necessary
centripetal force to keep
the ball going in a circle.
path of ball if the string
breaks

15. The net force is towards the center!
Centripetal Force
The force required to cause an object to follow a circular path.
Centripetal means “center seeking”
The net force is towards the center!

16. A car turning a corner…
MUST have a centripetal force in order to put it into a circular path!
Friction between the road and tires is the centripetal force.
No friction (ice) = No centripetal force 
This makes the car slide.

17. Centrifugal force
Centrifugal means “center fleeing.”
The red object will make the turn only if there is enough friction on it…otherwise it goes straight.
The apparent outward force is called the centrifugal force…
But it isn’t a force at all-it’s actually the absence of a centripetal force!!!
object on
the dashboard
straight line
object naturally
follows

18. Silly Silo (Rotor) Friction between Bart and wall Bart’s weight
wall pushing
in on Bart
Bart’s
weight
The inward wall force keeps Bart in the circle.
Friction keeps him from falling down.

19. Very little gravity in space…

20. Very little gravity in space…

21. But we can make our own to make it easier!
Space Station
But we can make our own to make it easier!
The faster it rotates, the more people will weigh.
The International Space Station

22. Ladybug on the inside of a bike tire…
Just like the space station, it would feel like gravity for the ladybug!!!
The faster the bike goes, the more the ladybug will weigh!

23. Ladybug on a Turntable Why??? Which ladybug has a greater velocity?
The inside ladybug.
The outside ladybug.
The outside ladybug!
Why???
It must cover more distance in the same amount of time!

24. Basically, the velocity depends on the radius.
Larger radius = larger velocity!
Smaller radius = smaller velocity!

25. Goal: The weight (N) hanging down = the Centripetal Force (N)
Lab Set Up
tape
Goal: The weight (N) hanging down = the Centripetal Force (N)