Transcript Chasing your tail for science.

Chasing your tail for science.
Moving
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Stand up.
Walk in a perfectly round path to your left.
Which way do you have to push with your
foot to walk in the circle?
Answer :
Toward the center of your path.
Pushing
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Using the ball at the front of the room.
Make the ball travel counterclockwise in a
circle around a pen at the lab tables.
Which way do you have to push to get the
ball to go in a circle?
Answer :
Toward the pen.
Circular motion
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You have just studied circular motion.
It has 2 dimensions.
Speed can be constant but velocity will
always change.
Moving in a circle causes velocity to
constantly change.
But which way?
Lets study!!!!!!!!!!!!!!!!!!!!!!!!
Vocab
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Circumference
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Period
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distance around a circle.
C = 2r
Units : meters (m)
time to complete one revolution along a
circular or repeating path.
Symbol: T
Unit : seconds (s)
Frequency
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number of rotations per second.
Symbol : f
Unit : Hertz (Hz)
Calculate speed
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To find speed, need to know distance and time.
Time for once around is the period, T
Distance for once around is circumference.
C=2pr
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So,
C 2pr
v 
T
T
Units are m/s
This is when moving at a constant speed.
Speed calculation
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A merry-go-round has a radius of 6.0 m and
takes 60 s to complete one revolution.
How fast is an ant traveling that is sitting at the
outer edge of the merry-go-round?
Give : T = 60 s, r = 6.0m
C 2pr 2p (6.0m)
v 
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T
T
60 s
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v = 0.628 m/s
Acceleration?
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What happens to the
velocity vector as you
move in a circle?
It changes direction.
You have zero
displacement for each
round trip.
Changing velocity
means, acceleration.
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Which way is it
changing?
Acceleration
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Velocity changes toward the
center.
Acceleration points toward
center of circular path.
Called Centripetal
Acceleration
Always toward center of
curved path for constant
speed.
Centripetal Acceleration
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Found by equation :
Where :
v = speed
r = radius
Acceleration depends
on both speed and
radius of path.
2
v
ac 
r
Centripetal Acceleration
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Find acceleration for merry-go-round.
v = 0.628 m/s, r = 6.0 m
So ac= (0.628 m/s)2/6.0m = 0.066 m/s/s
How would ac change if the velocity was
constant and the ant
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Moved toward center?
Acceleration will increase.
Moved away from center?
Acceleration will decrease.
Moved to center?
No acceleration. r = 0
True Force
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When you move in a circle, Which way are you
accelerating?
Toward the center.
Which way are you being pushed?
Toward the center.
What object is doing this?
The surface.
What is the sum of the forces?
Centripetal Force
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Unbalanced force responsible for circular
motion.
Always exerted toward center of path.
There is no object pushing you outward.
THERE IS NO CENTRIFUGAL FORCE EVER.
What makes you feel the fake effect?
Inertia.
Centripetal Force
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Found by using 2nd Law.
ΣF=ma
ΣFc=mac
2
v
Fc  m r
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This is the total sum of the forces which causes
circular motion.
Example
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Find the centripetal force exerted on you
when standing at the edge of the merrygo-round.
ac = 0.066m/s/s , m = 50 kg
ΣFc=mac
ΣFc=(50 kg)(0.066 m/s/s) = 3.3 N
Which way is this force exerted?
Toward Center of merry-go-round.
Why don’t I fall?
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Gravitron – centripetal force exerted by
the wall keeps you moving in a circle.
Friction between body and wall balances
the force exerted by Earth and you don’t
fall.
Rollercoaster loop – at top you do not fall
because track pulls the cars toward center
at g.