Download Circular Motion

Circular Motion
Physics
•Earth rotates about its axis
•Satellite revolves about the
earth
Part I-Intro to Circular Motion
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Tangential Speed and Velocity
Frequency and Period
Centripetal Force
Centripetal Acceleration
Characteristics of Circular
Motion
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Tangential (linear) Velocity
Frequency
Period
Frequency, f :
#revolutions per unit time
Units:
 Hertz (Hz)
 Cycles/sec
 rpm
r
Period
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Period T : time for 1 revolution
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Unit: sec, min, h
Relating Frequency and period
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f= 1
T
Arc Length
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Arc Length s (unit: meter)
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Distance traveled along a circular path.
s
Average Tangential (Linear) Speed
v= d
t
v= 2πr/T
Unit: m/s
Uniform Circular Motion
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Linear(tangential speed is constant)
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v=constant
Tangential (Linear) Velocity
The tangential velocity vector is
tangent to the circle at the point of
v
study.
v
Problem 1
vc=2(3.14)(r)/T
A biker travels once around a circular
track of radius 20.0m in 3s.
Calculate:
a)
the period
b)
the average tangential speed
Answers:
T = 3s,
Vc = 41.9m/s
Record Player
Problem 2
A coin sits 0.10m from the center of a
record player spinning at 45rpm.
a)
What is the period of the coin?
b)
What is the linear speed of the coin?
Answer: T=1.33s, vc=0.47m/s
Merry-go-Round
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?
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How does the f vary with r?
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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?
Centripetal Force, Fc= m v2
r
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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.
What forces represent the
centripetal force in these examples?
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Car on bend of road.
Coin on record player.
Child on merry-go-round.
Ball tied on a string.
Centripetal Acceleration, ac= v2
r
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Has same direction as centripetal
force.(Always points to the center).
Is perpendicular to the tangential
velocity at any given instant.
Centripetal Force
Fc=mac
Problem 3 Fc=mv2/r
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.
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Answer: 5.9N