Transcript Wed Lecture

Centripetal Acceleration and
Circular Motion
Circular Motion
B
A
C
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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Acceleration in Uniform
Circular Motion
v2
R
R
v1
v2
a
R
centripetal acceleration
Acceleration is due to change in direction, not speed.
Since turns “toward” center, must be a force toward
center.
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Acceleration in Uniform
Circular Motion
Draw in forces.
v1
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Common Incorrect Forces
SF = ma
 Force of Motion (Inertia not a force)
 Centrifugal Force (wrong object!)
 Centripetal Force (tension, gravity, friction,
 Acceleration:
normal)
Example: ball in vertical circle
Draw in forces.
v1=10m/s
A ball of mass 2kg is being swung in
a vertical circle with a speed of
10m/s. What is the tension in the
rope at the top of the circle?
g
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Example: ball in vertical circle
Draw in forces.
A ball of mass 2kg is being swung in
a vertical circle with a speed of
10m/s. What is the tension in the
rope at the bottom of the circle?
g
v1=10m/s
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Example
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 < mg
a=v2/R
B. FN = mg
C. FN > mg
R
correct
FN
v
mg
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Example: roller coaster
What is the minimum speed you must have at the
top of a 20 meter roller coaster loop, to keep
the wheels on the track.
Y Direction: F = ma
N
Let N = 0, just touching
mg
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Summary of Concepts

Uniform Circular Motion
 Speed is constant
 Direction is changing
 Acceleration toward center a = v2 / r
 Newton’s Second Law F = ma
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