1. Circular Motion
Physics
Mrs Coyle

2. Earth rotates about its axis
Satellite revolves about the earth

3. Part I-Intro to Circular Motion
Tangential Speed and Velocity
Frequency and Period
Centripetal Force
Centripetal Acceleration

4. Characteristics of Circular Motion
Tangential (linear) Velocity
Frequency
Period

5. Frequency, f : #revolutions per unit time
f = # rev / time
Units:
(1/sec)=sec-1=Hertz (Hz)
rpm (#rev/min)
rps (#rev/sec) r

6. Period Period T : time for 1 revolution Relating Frequency and period
Unit: sec, min, h
Relating Frequency and period
f= 1 T

7. Arc Length Arc Length s (unit: meter)
Distance traveled along a circular path. s

8. Average Tangential (Linear) Speed
v= s
t Unit: m/s
v= 2pr/T = 2prf

9. Uniform Circular Motion
Linear(tangential speed is constant)
v=constant

10. Tangential (Linear) Velocity
The tangential velocity vector is tangent to the circle at the point of study. v v

11. Problem 1 A biker travels once around a circular
track of radius 20.0m in 3s.
Calculate:
the average tangential speed
the frequency
the period
Answers: 41.9m/s, f=0.33Hz, T=3s
2.09rad/sec m/s f=0.33Hz T=3s

12. Record Player

13. Problem 2 A coin sits 0.10m from the center of a
record player spinning at 45rpm.
What is the frequency in Hertz?
What is the period?
What is the linear speed?
Answer: 0.75Hz, 1.33s, 0.47m/s

14. Merry-go-Round

15. How does the v vary with r?
The linear speed increases as r increases.
Example:
How does your linear speed change when you are on a merry-go-round and you move away from the center?

16. How does the f vary with r?
f does not depend on r
Example:
How does your frequency change when you are on a merry-go-round and you move away from the center?

17. Centripetal Force, Fc= m v2 r
Is a center seeking force. (Always points to the center.)
Is perpendicular to the tangential velocity at any given instant.
It is not an extra force. An existing force represents the centripetal force.

18. What forces represent the centripetal force in these examples?
Car on bend of road.
Coin on record player.
Child on merry-go-round.
Ball tied on a string.

19. Centripetal Acceleration, ac= v2 r
Has same direction as centripetal force.(Always points to the center).
Is perpendicular to the tangential velocity at any given instant.

20. Centripetal Force
Fc=mac

21. Problem 3 A child on a merry-go-round sits 1.5m
from the center. They spin 3 times in one
min. The mass of the child is 40kg.
Find the friction(centripetal force) acting on
the child.
Answer: 5.9N

22. Part II More Centripetal Force Problems
Car Rounding a Curve
Loop-the- loop
Rotor

23. What force plays the role of the centripetal force when a car rounds a curve?

24. Car Rounding a Bend

25. Example 1: Car Rounding a Curve
A car is travelling with a speed of 45km/h on a circular horizontal track of radius 50m. What is the minimum coefficient of friction, so that the car stays on the track?
Answer: 0.3

26. What force plays the role of the centripetal force when a ball is on the top of a loop-the-loop?

27. Loop the Loop

28. Example 2: Loop-the-loop
What is the critical velocity of a ball at the top of the loop of radius .3m so that it completes the loop?
Answer: 1.7m/s

29. Rotor Ride

30. Rotor Ride

31. What force plays the role of the centripetal force in the rotor ride?

32. Example 3: Rotor
A brave student rides in a rotor of radius 5m whose floor drops when it reaches a speed of 20mi/h. What is the coefficient of friction between the student and the wall of the rotor, so that the student does not fall? Answer: 0.6

33. Recap