Transcript Centripetal Acceleration and Gravitation Notes

Important situations in
circular motion
When accelerating, the feeling you
have is opposite the acceleration
This is why it feels like
there is centrifugal
acceleration when it’s
really centripetal
acceleration.
Centripetal force is the general name
given to the inward force
The centripetal force The centripetal force The centripetal force
IS THE
IS THE
IS THE
Tension
Friction
Force of Gravity
Notice the v and a are at right angles
This is always true for uniform circular motion
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Newton’s first law dictates that the object will
remain in straight line motion until a force cause
turning
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This is the view from above for a board with a
ball on it with and without a wall
As the cart turns, what happens to the ball?
A force toward
the center is
necessary to
cause turning.
How much acceleration?
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As you may have seen in the lab, centripetal
acceleration depends on two factors:
The speed of the object (v)
 The radius of the circular motion (r)
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The magnitude of centripetal acceleration can be
determined by the equation:
ac = v2/r
Other important measurements
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Period (T): The time it takes for one complete
rotation (measured in seconds)
Frequency (f): How many complete rotations
happen per second (measured in Hertz; 1 Hz =
1 rotation per second)
We could also calculate ac using period or
frequency (however, we won’t in this class)
Free Body for anything circling vertically
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Like a bucket of water
Both forces are down at the top
So doesn’t that mean the water will surely fall out?
Nope, inertia keeps the water moving in a straight line
The combined (net) forces are causing centripetal
acceleration – making it turn
Acceleration is not the same as motion! (recall braking
car – a is backwards but car moves forward)
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As the coaster goes around the loop the force
for turning, the track, must be into the center of
the loop.
What is the force from the track?
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The normal force!!
At the top of the loop what direction is the
normal force?
Down
 Both gravity and
the normal are directed
downward
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Any time there is turning
There must be an
unbalanced net force
causing an acceleration.
Remember Newton’s
F
nd
2
Law!!
= ma
For
centripetal force,
Fnet = mac
Orbiting
We know orbiting satellites have centripetal force
What is the centripetal force here?
Force of gravity
Is gravity here Fg=mg=m*9.8 m/s2?
NO!
Why not?
Too far from Earth for g=9.8m/s2
Is g = 0?
NO! g≠0 ever!
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You are in free fall, your “weightlessness” is due
to lack of a normal force
Your inertia moves you tangent to the orbital
path, but the gravity pulls you in
So how do you calculate the Fg?
Law of Universal Gravitation
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Legend has it that Newton thought “an apple
falls to the Earth because of the force of gravity.
At what distance does the force stop pulling?
Does the force of gravity pull on the moon?”
Eventually he realized that there must be a
gravitational force between every pair of objects
The amount of force depended on the masses of
the objects and the distance between them
Law of Universal Gravitation
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For an orbiting object
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F=ma
F= Fg = ma gravity is the only force
Fg = Gm1m2/r2 = ma
Gm1m2/r2 = ma = mv2/r
Same r’s so one cancels
One m is the mass of the object; it cancels
So all you need is the radius to find the velocity!
Gm1mearth/r2 = mv2/r so Gm2/r = v2
Try some multiple choice at
www.wiley.com/college/cutnell general site
 Specific to Ch. 5 self assessment
http://www3.interscience.wiley.com:8100/legacy/
college/cutnell/0471151831/sat/media/html/sa
t_c05/sat_c05.htm
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