Student
A. Ke y
Class
Date
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Circular Motion
1
~ Any object that revolves about a single point or axis undergoes circular motion
~ The speed of an object in a circular motion points along the tangent with the circle
~ The speed can be found using the formula v = ! = ~, where r is the radius of the
t
T
circle and T is the time, called period, needed for the object to complete one rotation
~ Centripetal acceleration is always directed toward the center and it is due to a
2
~
~
~
~
change in direction, and can be found using the formula ac = ~
T
Tangential acceleration is due to a change in speed
A uniform circular motion has a constant speed, therefore it has centripetal
acceleration only but not a tangential acceleration
The net force that is directed toward the center of the circle is called centripetal force
Using the Newton's second law for the centripetal force we can write Fe = mac
2
~ The formula for the centripetal force is Fc = ~
T
~ Centripetal force is simply the name given to the net force on an object in uniform
circular motion; it is not some special extra force that has to be there
~ Friction between a race cars tires and a circular track is a centripetal force that keeps
the car in a circular path
l
~ Gravitational force is a centripetal force that keeps Moon in its orbit around Earth
~ Inertia in circular motion is often misinterpreted as a force
1.
Identify the forces that contribute to the centripetal force on
the object in each of the following examples:
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a. a bicycList moving around a flat, circular track
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b. a bicycLe moving around a flat, circular track
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in the orbit around the Earth
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c. a race car turning a corner on a steeply banked curve
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d. a pLanet revolving around the Sun
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2.
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Explain what makes a passenger in a turning car slide toward the
door of the car.
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Pizza makers traditionally form the crust by throwing the dough
up in the air and spinning it. Why does this make the pizza crust
bigger? .
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Give an example of a situation in which an automobile driver can
have a centripetal acceleration but no tangential acceleration.
4.
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Why does mud fly off a rapidly turning wheel?
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6.
A rope attaches a tire to an overhanging tree limb. A girl
swinging on the tire has a.centripetal acceleration of 3.0 m/s2.
If the length of the rope is 2.1 m, what is the girl's
tangential speed?
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A bicyclist is riding at a tangential speed of 13.2 mls around a
circular track. The magnitude of the centripetal force is 377 N,
and the combined mass of the bicycle and the rider is 86.5 kg.
What is the track's radius?
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A dog sits 1.5 m from the center of a merry-go-round. The merrygo-round is set in motion, and the dog's tangential speed is 1.5
m/s. What is the dog's centripetal acceleration?
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A 905 kg car travels around a circular track with a circumference
of 3.25 km. If the magnitude of the centripetal force is 240 N,
what is the car's tangential speed?
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9.
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Tarzan tries to cross a river by swinging from one bank to the
other on a vine that is 10.0 m long. His speed at the bottom of
the swing is 8.0 m/s. Tarzan does not know that the vine has a
breaking strength of 1.0 x 103 N. What is the largest mass that
Tarzan can have and still make it safely across the river?
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