Announcements!

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Announcements!

• Extra credit posted this coming Sunday--get your
  team together!
• Mon/Tue-Circular applications of Newtons Laws
• Good examples in the book!
• Fuddruckers tomorrow (Tuesday) night
• Test this Thursday/Friday--practice test posted
  now!

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Centripetal Acceleration
An object moving in a circle of radius r w/
constant speed v has an acceleration directed
toward the middle of the circle, with a magnitude
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Centripetal Force!
Kinematics how things move Dynamics why
things move Objects moving in circles are
accelerating (centripetally), so the next
question is What causes centripetal
acceleration?
Fcentripetal
The answer centripetal force.
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Centripetal Force
Centripetal Force the center-seeking force
necessary to keep an object moving in a circle.
Its important to understand that centripetal
force is a general name used to describe any
force(s) that keep an object moving in a circle,
just like we use Fnet generally to describe the
forces that accelerate an object linearly. The
actual forces that make an object move
centripetally are due to things that weve
already discussed FTension for ropes, cords,
strings, etc., Fgravity for graviational force,
Ffriction for... friction, and (in some odd
cases) Fnormal, etc.
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Centripetal Force
Centripetal Force the center-seeking force
necessary to keep an object moving in a circle.
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Example
At the beginning of a hammer throw, a 5 kg mass
is swung in a horizontal circle of 2.0 m radius,
at 1.5 revolutions per second. What is the
centripetal force required to keep this object
moving in a horizontal circle? (Ignore the
vertical effect of gravity.)
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Cool problem

• Example A 1000 kg car on a flat road is
  traveling at 14 m/s.
• On a curve of radius 50m, what centripetal force
  will be necessary to keep the car on the road?
• b. If the µ static for this road is 0.60, will
  the car make the turn?
• c. If the µ static for the road is 0.20, will the
  car make the turn?
• d. What is the maximum speed the car can have and
  still make the turn?

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Advanced Cool Problem

• Example A 1000 kg car on a flat road is
  traveling at 14 m/s.
• d. How high should we bank the turn if we want
  the car to be able to stay on with no friction?

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How the heck...? Problem
Example A small body of mass m is suspended from
a string of length L which makes an angle ? with
the vertical. The body revolves in a horizontal
circle. Find the speed of the body and the period
(time) of one revolution in terms of L, ?, and
fundamental constants.
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Vertical Circles
Objects that are traveling in vertical circles
are treated exactly the same as objects traveling
in horizontal circles the sum of the centripetal
forces adds up to allow the object to accelerate
centripetally, and thus, travel in a circle.
(?Fcmac)
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Vertical Circles
One obvious challenge is that the Tension in the
rope (in this example) is no longer the only
force that is a factor in the balls circular
motion--the force of gravity now has to be taken
into account.
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Vertical Circles

• Example A 1.8-kg ball is being swung in a
  vertical circle, at the end of a 1.2-m long rope.
• What is the minimum velocity the ball can have at
  the top of its circular path?
• What is the Tension in the rope as the ball
  swings past the bottom of the path at 5.0 m/s?

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Vertical Circles

1. What is the minimum velocity the ball can have at
   the top of its circular path?

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Vertical Circles

1. What is the minimum velocity the ball can have at
   the top of its circular path?

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Vertical Circles
b. What is the Tension in the rope as the ball
swings past the bottom of the path at 5.0 m/s?
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Vertical Circles
b. What is the Tension in the rope as the ball
swings past the bottom of the path at 5.0 m/s?
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So... what is centrifugal force?
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Centrifugal Force
Centrifugal force is an apparent force--a fake
force!--that we mistakenly think pulls an object
away from the center of the circle. There is no
force pulling the ball outward!!!
If youre holding on to the string attached to
the ball while it goes in a circle, its true
that your hand feels an outward pull this is due
to Newtons 3rd Law (your hand pulls on the ball
to keep it moving in a circle, the ball pulls
back on your hand).
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Centrifugal Force
It may help to think about what happens when we
let go of the string does the ball go flying
away from the center of the circle, due to the
mysterious, fake, centrifugal force? No! It
continues to travel in a straight line from the
point where it was let go. The fake centrifugal
force is due to balls inertia.
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Non-Uniform Circular Motion
Earlier, we said that an object moving in a
circle can have radial and tangential
accelerations. These obviously result from
radial and tangential forces. Calculate the
radial and tangential forces acting on the
billiard ball, in terms of m, v, r, and Ø (angle
from vertical).