Download Circular Motion Powerpoint

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 bowling ball and broom at the front of
the room.
Make the ball travel counterclockwise around the
“space” in the center of the room.
Which way do you have to push to get the ball
to go around the faucets?
Answer :
Toward the middle of the space.
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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First, vocab word.
Period – time to complete one revolution
along a circular or repeating path.
Symbol: T
Unit : s
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Circumference – distance around a circle.
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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 of 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 

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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circular motion1.IP
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.
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circular
motion3.IP
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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So ac= (0.628 m/s)2/6.0m = 0.066 m/s/s
How would ac change if
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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 is a force acting on you?
Toward the center.
What force is doing this?
Friction.
What is the net force?
Centripetal Force
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Net force responsible for circular motion.
Always acts toward center of path.
There is no outward acting force.
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.
F=ma
Fc=mac
2
v
Fc  m
r
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This is the net force which causes circular motion.
Example
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Find the centripetal force acting on you
when standing at the edge of the merrygo-round.
ac = 0.066m/s/s , m = 50 kg
Fc=mac
Fc=(50 kg)(0.066 m/s/s) = 3.3 N
Which way is this force acting?
Toward Center of merry-go-round.
Why don’t I fall?
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Gravitron – centripetal force provides the
normal force. Friction between body and
wall equals weight and you don’t fall.
Rollercoaster loop – at top you do not fall
because track accelerates cars toward
center at g.
Circular Motion – Practical
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You cannot sense constant velocity, but you
can sense acceleration (changing velocity; speed
OR direction).
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Park ride, elevator, bad plane ride
The change in velocity (acceleration) is ALWAYS
toward the center
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Proportional the the speed squared
Inversely proportional to the radius
Proportional
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As one gets bigger, the other gets bigger
Since “v” is squared, that means it doesn’t
matter which direction (clockwise or
counterclockwise) or whether you are
slowing down or speeding up…the bigger
the “change”, the bigger the acceleration
Inversely proportional
As the radius (how far you are away from
the center) increases the centripetal
acceleration decreases.
As the radius gets smaller, the acceleration
increases…BUT, at the CENTER…there is
NO acceleration…!
Why measure the period?
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The period is easy to measure, the
velocity is much harder to measure
Period is the time required to travel the
same distance as the circumference of a
circle.
Acceleration and Force
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How do we know the force is “toward the
center”, if we feel like the force is “outward”.
Acceleration cannot happen without a force.
Force MUST be in the same direction as the
acceleration.
Why does it travel like a projectile
after you release the “string”?
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Only one force is acting on it…What is it?
The moon circles the Earth in an almost
perfect circle…what is the force acting
upon the moon that causes it to do this?
What would happen if the moon were
closer? Further away?
Problem
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A 0.013 kg rubber stopper is attached to a
0.93 m length of string. The stopper is
swung in a horizontal circle, making one
revolution in 1.18 s
Find the speed of the stopper.
Find the centripetal acceleration
Find the force the string exerts on it.
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What do we know:
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Mass of stopper 0.013 kg
Circle radius, r 0.93 m
Period, T = 1.18
What do we need to know?
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Speed, v
Acceleration, ac
Force, Fc
Equations
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See handout for these equations
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Velocity = circumference / T
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Acceleration = (velocity)2/radius
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Force, Fc = mass (of stopper, kg)* acceleration
The Lab – Centripetal Force
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Centripetal force can only be measured
indirectly!
Why don’t we use the mass of the
stopper?..easier to use “force downward” .
Why does this work?
The Lab (cont)
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Because gravity is exerting an acceleration downward on
the washers (which have mass)
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Weight is a force = m*g (acceleration due to gravity)
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The weight (force) must = the “tension” that is exerted
on the string, since the string is not moving (up and
down)
Since we are “spinning” the cork and the string is
“stationary” (force down = tension centripetal force) .