Introduction to Circular Motion · Web viewTerm Definition Centripetal Force Centripetal Acceleration Rotate Revolve Linear Speed Angular Speed Center of Gravity Speed and Velocity

Vocabulary

Term DefinitionCentripetal Force

Centripetal Acceleration

Rotate

Revolve

Linear Speed

Angular Speed

Center of Gravity

Speed and VelocityRead 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:

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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 = 21.2-meter) 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.

Circular Motion and InertiaRead 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

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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:

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.

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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 Putt-Putt 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.

Speed and Velocity

1. What is uniform circular motion?

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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

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accelerated.

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

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traveling in a circle? (Hint: the formula involves mass, velocity and radius.)

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.

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4. What is Kepler’s 3rd law of planetary motion?

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

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?

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ac

v2

R

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.

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.

Class Work1. 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

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ac

v2

R

Fc=mv2/R

B. What is the centripetal acceleration?Looking For Given Relationship Solution

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?



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?



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.


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?


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B. Calculate the centripetal acceleration?Looking For Given Relationship Solution

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.


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.


B. Calculate the centripetal acceleration of the stone.Looking For Given Relationship Solution

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.


B. Determine the centripetal force acting on the car.Looking For Given Relationship Solution

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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: _____

Rotate vs. RevolveWhat 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

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Linear speed is the distance traveled per unit of time.

Linear speed = 2πR(# of rotations) / timeor

Linear speed = 2πR(# of revolutions) / time

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Angular vs. Linear SpeedHow is the angular and linear speed of the Burt and Ernie below similar or different?

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 Work1. A wheel makes 10 revolutions in 5 seconds. Find its angular speed in rotations per second.


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?


(b) What is your linear speed in meters per second?Looking For Given Relationship Solution

3. A compact disc completes 60 rotations in 5 seconds.a. What is its angular speed?


Group Work

Burt

Ernie

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.


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?


7. Find the angular speed of a ferris wheel that makes 12 rotations during 3 minute ride. Express your answer in rotations per minute.


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.


HomeWork1. A wheel makes 20 revolutions in 5 seconds. Find its angular speed in rotations per second.


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?


(b) What is your linear speed in meters per second?Looking For Given Relationship Solution

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.


4. A merry-go-round makes 30 rotations in 3 minutes. What is its angular speed in rpm?Looking For Given Relationship Solution

Documents

Introduction to Circular Motion · Web viewTerm Definition Centripetal Force Centripetal Acceleration Rotate Revolve Linear Speed Angular Speed Center of Gravity Speed and Velocity