Uniform Circular Motion

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Uniform Circular Motion
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Circular Motion ACT 1
B
C
A
v
Answer B
A ball is going around in a circle attached to a
string. If the string breaks at the instant
shown, which path will the ball follow?
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Circular Motion
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Uniform Circular Motion
For a particle in uniform circular motion, the
velocity vector v remains constant in magnitude,
but it continuously changes its direction.
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Acceleration in Uniform Circular Motion
aave Dv / Dt Acceleration toward center
Acceleration is due to change in direction, not
speed. Object turns toward center ? must be a
force on object toward center.
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Centripetal Acceleration
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Centripetal Acceleration ACT
Which motion has the largest centripetal
acceleration?
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Preflight

• Consider the following situation You are driving
  a car with constant speed around a horizontal
  circular track. On a piece of paper, draw a Free
  Body Diagram (FBD) for the car. How many forces
  are acting on the car? A) 1 B) 2 C) 3
  D) 4

0 28 44 28
Gravity, Normal Force, Friction
Fn Normal Force, W Weight, the force of
gravity, f centripetal force.
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Common Incorrect Responses

• Acceleration SF ma
• Centripetal Acceleration
• Force of Motion (Inertia not a force)
• Forward Force,
• Force of velocity
• Speed
• Centrifugal Force (No such thing!)
• Centripetal (really acceleration)
• Inward force (really friction)
• Internal Forces (dont count, cancel)
• Car
• Engine

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Circular Motion Requires Net Force
Net force may be provided by the tension in a
string, the normal force, or friction, among
other sources as with any net force.
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Preflights

• Consider the following situation You are driving
  a car with constant speed around a horizontal
  circular track. On a piece of paper, draw a Free
  Body Diagram (FBD) for the car. The net force on
  the car is

A. Zero B. Pointing radially inward C.
Pointing radially outward
22 6711
This is why many racetracks have banked
roadways
Centripetal force is always pointing inward"
Ever spin stuff in a bowl? It gravitates
outward.
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Dip ACT

• Suppose you are driving through a valley whose
  bottom has a circular shape. If your mass is m,
  what is the magnitude of the normal force FN
  exerted on you by the car seat as you drive past
  the bottom of the hill A. FN lt mg B. FN mg
  C. FN gt mg

v
SF ma FN - mg mv2/R FN mg mv2/R
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Dip Example
While driving on a country road at a constant
speed of 17.0 m/s, you encounter a dip in the
road. The dip can be approximated by a circular
arc with a radius of 65.0 m. What is the normal
force exerted by the car seat on an 80.0 kg
passenger at the bottom of the dip?
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Merry-Go-Round ACT

• Bonnie sits on the outer rim of a merry-go-round
  with radius 3 meters, and Klyde sits midway
  between the center and the rim. The
  merry-go-round makes one complete revolution
  every two seconds.
• Klydes speed is

Klyde
Bonnie
(a) the same as Bonnies (b) twice
Bonnies (c) half Bonnies
Bonnie travels 2 p R in 2 seconds vB 2
p R / 2 9.42 m/s Klyde travels 2 p (R/2) in
2 seconds vK 2 p (R/2) / 2 4.71 m/s
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Rounding a Corner
A 1,200 kg car rounds a corner of radius r 45.0
m. If the coefficient of friction between the
tires and the road is ms 0.82, what is the
maximum speed the car can have on the curve
without skidding?
Question How does this result depend on the
mass of the car?
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Banked Curves
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Revolving in a Circle
An energetic father places his 20 kg child in a
5.0 kg cart to which is attached a 2.0 m long
rope. He then holds the end of the rope and
spins the cart and child in a circle, keeping the
rope parallel to the ground. If the tension in
the rope is 100 N, what is the carts tangential
speed?
Vertical
m 25 kg r 2 m T 100 N v ?
Radial
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50 Driving in your car with a constant speed
of 12 m/s, you encounter a bump in the road that
has a circular cross-section, as indicated in
Figure 630. If the radius of curvature of the
bump is 35 m, find the apparent weight of a 67-kg
person in your car as you pass over the top of
the bump.
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51 Referring to Problem 50, at what speed must
you go over the bump if people in your car are to
feel weightless?
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Centrifuge
A centrifuge rotates at a rate such that the
bottom of a test tube travels at a speed of 89.3
m/s. The bottom of the test tube is 8.50 cm from
the axis of rotation. What is the centripetal
acceleration acp at the bottom of the test tube
in m/s and in g (where 1 g 9.81 m/s2)?