Download Introduction to Circular Motion

Vocabulary
Term
Centripetal Force
Definition
Centripetal
Acceleration
Rotate
Revolve
Linear Speed
Angular Speed
Center of Gravity
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Speed and Velocity
Read from Lesson 1 of the Circular and Satellite Motion chapter at The Physics Classroom:
http://www.physicsclassroom.com/class/circles/Lesson-1/Speed-and-Velocity
Review:
1. A quantity that is fully described by magnitude alone is a ___________ quantity. A quantity that is fully described by both
magnitude and direction, is a ___________ quantity.
a. scalar, vector b. vector, scalar
2. Speed is a ____________ quantity. Velocity is a ____________ quantity.
a. scalar, vector b. vector, scalar
c. scalar, scalar
d. vector, vector
3. State the equation for calculating the average speed of an object:
Circular Motion:
4. An object that moves uniformly in a circle can have a constant ___________________ but a changing
___________________.
a. speed, velocity
b. velocity, speed
5. The direction of a velocity vector is always ______. Circle all that apply.
a. in the same direction as the net force that acts upon it
b. in the opposite direction as the net force that acts upon it
c. in the same direction as the object is moving
d. in the opposite direction as the object is moving
e. ... none of these!
6. True or False:
The direction of the velocity vector of an object at a given instant in time depends on whether the object is speeding up or
slowing down.
7. For an object moving in uniform circular motion, the velocity vector is directed _____.
a. radially inwards towards the center of the circle
b. radially outwards away from the center of the circle
c. in the direction of the tangent line drawn to the circle at the object's location
8. Use your average speed equation to determine the speed of ... . (Given: Circumference = 2•PI•R)
a. ... a rider on a carousel ride that makes a complete revolution around the circle (diameter = 21.2meter) in 17.3 seconds. PSYW
b. ... your clothes that are plastered to the wall of the washing machine during the spin cycle. The
clothes make a complete revolution around a 0.35 meter circle in 0.285 seconds. PSYW
9. A roller coaster car is traveling over the crest of a hill and is at the location shown. A side view is shown at the right.
Draw an arrow on the diagram to indicate the direction of the velocity vector.
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Circular Motion and Inertia
Read from Lesson 1 of the Circular and Satellite Motion chapter at The Physics Classroom:
http://www.physicsclassroom.com/Class/circles/u6l1c.html
http://www.physicsclassroom.com/Class/circles/u6l1d.html
Review Questions:
1. Newton's first law states: An object at rest will
An object in motion will
unless acted upon by
2. Inertia is ...
Applications of Newton's First Law to Motion in Circles:
The diagram below depicts a car making a right hand turn. The driver of the car is represented by the
circled X. The passenger is represented by the solid circle. The seats of the car are vinyl seats and have
been greased down so as to be smooth as silk. As would be expected from Newton's law of inertia, the
driver continues in a straight line from the start of the turn until point A. The path of the driver is shown:
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Rex Things and Doris Locked are out on a date. Rex makes a rapid right-hand turn. Doris begins sliding across the vinyl
seat (which Rex had waxed and polished beforehand) and collides with Rex. To break the awkwardness of the situation,
Rex and Doris begin discussing the physics of the motion that was just experienced. Rex suggests that objects that move
in a circle experience an outward force. Thus, as the turn was made, Doris experienced an outward force that pushed her
towards Rex. Doris disagrees, arguing that objects that move in a circle experience an inward force.
In this case, according to Doris, Rex traveled in a circle due to the force of his door pushing him inward. Doris did not
travel in a circle since there was no force pushing her inward; she merely continued in a straight line until she collided
with Rex. Who is correct? ________ Argue one of these two positions.
Noah Formula guides a golf ball around the outside rim of the green at the Hole-In-One PuttPutt Golf Course. When the ball leaves the rim, which path (1, 2, or 3) will the golf ball
follow? Explain why.
Suppose that you are a driver or passenger in a car and you travel over the top of a small hill in the road at a high speed.
As you reach the crest of the hill, you feel your body still moving upward; your gluts might even be pulled off the car
seat. It might even feel like there is an upward push on your body. This upward sensation is best explained by the
______.
a. tendency of your body to follow its original upward path
b. presence of an upward force on your body
c. presence of a centripetal force on your body
d. presence of a centrifugal force on your body
Darron Moore is on a barrel ride at an amusement park. He enters the barrel and stands on a
platform next to the wall. The ride operator flips a switch and the barrel begins spinning at
a high rate. Then the operator flips another switch and the
platform drops out from
under the feet of the riders. Darron is plastered to the wall of the barrel. This sticking to the
wall phenomenon is explained by the fact that ________.
a. the ride exerts an outward force on Darron which pushes him outward against the wall
b. Darron has a natural tendency to move tangent to the circle but the wall pushes him inward
c. air pressure is reduced by the barrel's motion that causes a suction action toward the wall
d. the ride operator coats the wall with cotton candy that causes riders to stick to it
Always take time to reflect upon your own belief system that governs how you interpret the physical world. Be aware of your
personal "mental model" which you use to explain why things happen. The idea of this physics course is not to acquire
information through memorization but rather to analyze your own preconceived notions about the world and to dispel them for
more intelligible beliefs. In this unit, you will be investigating a commonly held misconception about the world - that motion in a
circle is caused by an outward (centrifugal) force. This misconception or wrong belief is not likely to be dispelled unless you
devote some time to reflect on whether you believe it and whether it is intelligible. After considering more reasonable beliefs, you
will be more likely to dispel the belief in a centrifugal force in favor of a belief in an inward or centripetal force.
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Speed and Velocity
1. What is uniform circular motion?
2. What is the formula to calculate the average speed for an object traveling in a circular path?
3. How are average speed and radius related?
4. How do speed and velocity differ?
5. Draw a picture showing the direction of an object’s velocity when traveling in a circular path.
6. Used words to describe the direction of the velocity vector.
7. Summarize the differences between an object’s speed and velocity while moving in uniform circular
motion.
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Acceleration
1. What is a common misconception about the speed of an object moving in a circle?
2. How does an object accelerate when it moves in a circle if its speed is constant?
3. Draw a picture showing the direction of an object’s acceleration when traveling in a circular path.
4. What type of device is used to measure the acceleration of an object?
5. Identify three controls on an automobile that allow the car to be accelerated.
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The Centripetal Force Requirement
1. What does the word “centripetal” mean?
2. Explain how inertia relates to the motion of an object traveling in a circle.
3. Draw a picture showing the direction of the centripetal force acting up an object when traveling in
a circular path.
4. List three real world examples of centripetal force.
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The Forbidden F-Word
1. How does the word “centrifugal” differ from “centripetal?”
2. What is a common misconception about students moving in circular motion?
3. What “law” explains the feeling of an outward force? Explain.
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Mathematics of Circular Motion
1. What is the formula to calculate the average speed of an object moving in a circle?
2. What is the primary formula to determine the acceleration of an object moving in a circle? (Hint: the formula
involving velocity and radius.)
3. What is the primary formula used to calculate the net force acting upon an object traveling in a circle? (Hint: the
formula involves mass, velocity and radius.)
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Kepler’s Three Laws
1.
Who proposed the three laws of planetary motion?
2. What is Kepler’s 1st law of planetary motion?
3. What is Kepler’s 2nd law of planetary motion? Draw a picture to show how any planet sweeps out equal areas in
equal amounts of time.
4. What is Kepler’s 3rd law of planetary motion?
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Centripetal Force (Fc)
What is centripetal force?
•Some physical force pushing or pulling the object towards the __________________ of the circle.
•The word "centripetal" is merely an adjective used to describe the _______________ of the force.
• Without the centripetal force, the object will move in a __________________ line.
• Centripetal force is any force that causes an object to move in a circle.
• To calculate centripetal force:
Fc=mv2/R
• To calculate centripetal acceleration:
ac=v2/R
v2
ac
R
Give three examples of centripetal force.
 As a car makes a turn, the force of ____________________________ acting upon the turned wheels of the
car provide the centripetal force required for circular motion.
 As the moon orbits the Earth, the force of _________________________ acting upon the moon provides the
centripetal force required for circular motion.
 What three factors affect the centripetal force of an object moving in a circle?
1._______________
2._______________
3._______________
 In the picture below Stewy swings Peter in a circle. Label the following with arrows: the direction of the
centripetal force, the direction of Peter’s acceleration, and the direction Peter would travel if Stewy let go.
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But what about centrifugal forces?
• There is no such thing! The sensation of an outward force and an outward acceleration is a false sensation.
• For example, if you are in a car make a right turn, while the car is accelerating inward, your body continues in a
__________________ line. If you are sitting on the passenger side of the car, then eventually the outside door of
the car will hit you as the car turns inward. In reality, you are continuing in your straight-line inertial path tangent to
the circle while the car is accelerating out from under you.
• It is the ___________________________ of your body - the tendency to resist acceleration - which causes it to
continue in its forward motion. There is no physical object capable of pushing you outwards. You are merely
experiencing the tendency of your body to continue in its path ______________________ to the circular path along
which the car is turning.
Fc=mv2/R
v2
ac
R
Class Work
1. A 300-kg waterwheel rotates about its 20-m radius axis at a rate of 3 meters per second.
A. What is the centripetal force requirement?
Looking For
Given
Relationship
Solution
Given
Relationship
Solution
B. What is the centripetal acceleration?
Looking For
2. A 10-kg mass is attached to a string and swung horizontally in a circle of radius 3-m. When the speed of the mass reaches 8.1
m/s, what is the centripetal force requirement?
Looking For
Given
Relationship
Solution
3. A motorcycle travels 12.126 m/s in a circle with a radius of 25.0 m.
A. How great is the centripetal force that the 235-kg motorcycle experiences on the circular path?
Looking For
Given
Relationship
Solution
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B. What is the centripetal acceleration?
Looking For
Given
Relationship
Solution
Group Work
4. A 72-kg woman rides a bicycle in a 75.57-km circumference circle at a rate of 0.25 m/s.
A. What is the centripetal force experienced by the woman?
Looking For
Given
Relationship
Solution
Given
Relationship
Solution
B. What is the centripetal acceleration?
Looking For
5. A 25-kg mass swings on a string with a length of 2.4-m so that the speed at the bottom point is 2.8 m/s. Calculate the
centripetal force.
Looking For
Given
Relationship
Solution
6. A 65-kg mass swings on a 44-m long rope. If the speed at the bottom point of the swing is 12 m/s,
A. What is the centripetal force experienced by the mass?
Looking For
Given
Relationship
Solution
Given
Relationship
Solution
B. Calculate the centripetal acceleration?
Looking For
7. Determine the centripetal force acting on an 1100-kg car that travels around a highway curve of radius 150 m at 27 m/s.
Looking For
Given
Relationship
Solution
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HomeWork
1. The diagram below represents a 0.40-kilogram stone attached to a string. The stone is moving at a constant
speed of 4.0 meters per second in a horizontal circle having a radius of 0.80 meter.
A. Calculate the centripetal force acting on the stone.
Looking For
Given
Relationship
Solution
Relationship
Solution
B. Calculate the centripetal acceleration of the stone.
Looking For
Given
2. A 900-kg car moving at 10 m/s takes a turn around a circle with a radius of 25.0 m.
A. Determine the centripetal acceleration of the car.
Looking For
Given
Relationship
Solution
Relationship
Solution
B. Determine the centripetal force acting on the car.
Looking For
Given
3. According to the diagram of the plane below, the direction of the centripetal force on the airplane is directed toward:
_____
4. According to the diagram of the plane below, the direction of the acceleration on the airplane is directed toward: _____
5. According to the diagram of the plane below, the direction the plane would travel if a centripetal force was no longer
applied is toward: _____
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Rotate vs. Revolve
What is the difference between rotating and revolving?
 An object rotates about its axis when the axis is internal. List three examples of an object that rotates:

An object revolves when it moves around an external axis. List three examples of an object that revolves:
Angular Speed vs. Linear Speed
 Angular speed is the rate at which something turns. The rpm, or rotation per minute, is commonly used for
angular speed.
Angular speed = # of rotations / time
Or
Angular speed = # of revolutions / time

Linear speed is the distance traveled per unit of time.
Linear speed = 2πR(# of rotations) / time
or
Linear speed = 2πR(# of revolutions) / time
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Angular vs. Linear Speed
How is the angular and linear speed of the Burt and Ernie below similar or different?
Burt
Ernie
Each point on a rotating object has the same angular speed thus Burt and Ernie have the same angular speed.
The linear speed of a person on a merry-go-round is the distance traveled around the circle divided by the time.
The linear speed depends on the radius of the circle in which the person moves. Burt moves in a circle with the
largest radius, so his linear speed is the fastest.
Two people sitting at different places on the same merry go-round always have the same angular speed. But the
person sitting farther from the center has the faster linear speed.
Class Work
1. A wheel makes 10 revolutions in 5 seconds. Find its angular speed in rotations per second.
Looking For
Given
Relationship
Solution
2. You are sitting on a merry-go-round at a distance of 3 meters from its center. It spins 15 times in 3
minutes. (a) What is your angular speed in revolutions per minute?
Looking For
Given
Relationship
Solution
Relationship
Solution
Relationship
Solution
(b) What is your linear speed in meters per second?
Looking For
Given
3. A compact disc completes 60 rotations in 5 seconds.
a. What is its angular speed?
Looking For
Given
Group Work
4. A compact disc has a radius of 0.06 meters. If the cd rotates 4 times per second, what is the linear speed
of a point on the outer edge of the cd? Give your answer in meters per second.
Looking For
Given
Relationship
Solution
5. A merry-go-round makes 18 rotations in 3 minutes. What is its angular speed in rpm?
Looking For
Given
Relationship
Solution
6. Dwayne sits two meters from the center of a merry-go-round. If the merry-go-round makes
one revolution in 10 seconds, what is Dwayne’s linear speed?
Looking For
Given
Relationship
Solution
7. Find the angular speed of a ferris wheel that makes 12 rotations during 3 minute ride. Express your
answer in rotations per minute.
Looking For
Given
Relationship
Solution
8. Mao watches a merry-go-round as it turns 27 times in 3 minutes. The angular speed of the merry-go-round is
____ rpm.
Looking For
Given
Relationship
Solution
HomeWork
1. A wheel makes 20 revolutions in 5 seconds. Find its angular speed in rotations per second.
Looking For
Given
Relationship
Solution
2. You are sitting on a merry-go-round at a distance of 2.5 meters from its center. It spins 15 times in 3
minutes. (a) What is your angular speed in revolutions per minute?
Looking For
Given
Relationship
Solution
Relationship
Solution
(b) What is your linear speed in meters per second?
Looking For
Given
3. A compact disc has a radius of 0.06 meters. If the cd rotates once every second, what is the linear speed
of a point on the outer edge of the cd? Give your answer in meters per second.
Looking For
Given
Relationship
Solution
4. A merry-go-round makes 30 rotations in 3 minutes. What is its angular speed in rpm?
Looking For
Given
Relationship
Solution