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```PHYSICS STUDY GUIDE
CHAPTER 7: CIRCULAR MOTION
TOPICS:
• Circular Motion
WHAT YOU MUST KNOW
• An objects in uniform circular motion moves with constant speed, but changing velocity (direction
is always changing).
• An objects in uniform circular motion is acceleration
• Direction of Centripetal Force
• Direction of Centripetal Acceleration
• Direction of tangential velocity
DEFINITIONS
•
Circular Motion: Motion of an object that follows a circular path.
•
Centripetal Force: ANY force that keeps an object moving in a circle
•
Period (T): Time for an object to complete one entire revolution (rotation, cycle, etc).
PHYSICAL QUANTITIES
SYMBOL
c
r
T
vT
aC
FC
NAME
Circumference
Period
Tangential Velocity
Centripetal acceleration
Centripetal force
UNITS
Meters ( m )
Meters ( m )
Seconds ( s )
Meters per second ( m/s )
Meters per second squared ( m/s2 )
Newtons ( N )
MATHEMATICAL MODELS
•
Circumference
•
Tangential velocity
vT =
•
Centripetal acceleration
•
Centripetal Force
FEonO = g · m
C=2·π·r
•
Force of Earth
2 · π ·r
T
v2
ac =
r
•
Force of Static Friction
•
Coefficient of Static Friction
FC = m
FS = µS · FN
μS =
v2
r
or
v2
(r · g)
FC = m ⋅ ac
SOURCES OF CENTRIPETAL FORCE
The direction of the velocity of an
object moving in circular motion is
always “tangent to the circle”
The direction of the acceleration of
an object moving in circular motion
is always “towards the center of the
circle”
The direction of the force of an
object moving in circular motion is
always “towards the center of the
circle”
SOURCES OF CENTRIPETAL FORCE
SOURCE
FORCE DIAGRAM
REAL LIFE
CONECTION
• Dryer
• Rollercoaster
Normal force
• Ferris wheel
FC = FN
Classroom examples:
• Wooden track
• Bowling ball + mallet
• Pocket of a lacrosse
stick
• Any vehicle going
around a level
circular track.
Force of Static Friction
FC = FS
• Merry go round
Classroom examples:
• Record Player
FT
center
FTY
• Swings at
amusement parks
FC = FTX
Tension force
FC = FT
FEonO
Classroom examples:
• Wiffle ball attached to a string
• Plane attached to a string
• Amusement park
NOTE:
FTY holds up the object
and balances out FEonO.
FC = FTX
• Planets around suns
Gravitational force
• Moons or satellites
around planets
FC = FG
Classroom examples:
• Person on Earth’s surface
Magnetic force
FC = FB
N/A
• Particle accelerator
• Aurora Borealis
(Northern Lights)
VERTICAL CIRCLES
Five cases of an object moving in uniform circular motion in a vertical circle.
The system is the person.
REPRESEN
TATION
I
II
III
IV
V
SKETCH
FN
FN
FC
FORCE
DIAGRAM
FC
FC
FEonO
FN
FEonO
DIRECTIO
N OF
CENTRIPE
TAL
FORCE
MATHEMA
TICAL
MODEL
FEonO
UP
(POSITIVE)
DOWN
(NEGATIVE)
- FSonP – FEonP = - FC
+ FSonP – FEonP = + FC
+ FSonP – g·m = +
m·
DOWN
(NEGATIVE)
v2
r
- FSonP – g·m = -
m·
UP
(POSITIVE)
+ FSonP – FEonP = + FC
+ FSonP – FEonP = - FC
v2
r
+ FSonP – g·m = -
m·
DOWN
(NEGATIVE)
v2
r
+ FSonP – g·m = +
m·
+ FSonP – FEonP = - FC
v2
r
+ FSonP – g·m = -
m·
v2
r
```
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