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
 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= 2πr/T = 2πrf

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

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

11. Problem 1
A biker travels once around a circular
track of radius 20.0m in 3s.
Calculate:
a) the average tangential speed
b) the frequency
c) the period
Answers: 41.9m/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.
a) What is the frequency in Hertz?
b) What is the period?
c) 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. What force plays the role of the
centripetal force in the rotor ride?

http://upload.wikimedia.org/wikipedia/commons/7/7d/Rotormidcyclelunapraksyd.JPG

31. 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