Introduction to Circular Motion - Northern Highlands · Web viewAn object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. While

Vocabulary

Term DefinitionCentripetal Force A force that causes an object to move in a circle.

Centrifugal Force The effect of inertia on an object moving in a circle.

Centripetal Acceleration

The rate of change of speed of an object moving in a circle.

Rotate To spin around an axis of rotation that passes through an object.

Revolve To move around, or orbit, an external axis.

Linear Speed The distance traveled per unit of time.

Angular Speed The rate at which an object rotates or revolves.

Center of Gravity The average position of an object’s weight.

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: distance/time 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 (radius = 10.6-meter) in 17.3 seconds. PSYW

Looking For Given Relationship Solution

speed Distance=2πR=2π(10.6)Time=17.3 seconds

Speed = distance/time 3.85 m/s

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. PSYWLooking For Given Relationship Solution

speed Distance=2πR=2.19 meterTime=0.285 seconds

Speed = distance/time 7.72 m/s

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.

10.

Circular Motion and Inertia

Review Questions: 1. Newton's first law states: An object at rest will remain at rest.

An object in motion will stay in motion at constant speed in a straight line

unless acted upon by an unbalanced force.

2. Inertia is ... the tendency of an object to resist changes to its state of motion.

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. 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. Doris would be correct. There is no such thing as an “outward” force. The reason why this happens is due to an object’s inertia or the tendency to continue moving in a straight line.

BF

Direction of force

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.

The ball will follow path 2 due to the ball’s inertia (the tendency to continue moving in a straight line).

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?The motion of an object in a circle with a constant or uniform speed.

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?Average speed and radius are directly related. If you double the radius then the average speed doubles. If you triple the radius, then the average speed

triples, and so on.

4. How do speed and velocity differ?Speed is a scalar quantity and velocity is a vector quantity. Thus, speed has magnitude only while velocity includes both magnitude and direction.

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.The directions of the velocity vector at every instant is in a direction tangent to

the circle.

7. Summarize the differences between an object’s speed and velocity while moving in uniform circular motion.An object moving in uniform circular motion is moving around the perimeter

of the circle with a constant speed. While the speed of the object is constant, its velocity is changing. Velocity, being a vector, has a constant magnitude but a changing direction. The direction is always directed tangent to the circle and as the object turns the circle, the tangent line is always pointing in a new direction.

Acceleration

1. What is a common misconception about the speed of an object moving in a circle?An object moving in uniform circular motion is moving in a circle with a uniform

or constant speed. The velocity vector is constant in magnitude but changing in direction. Because the speed is constant for such a motion, many students have

the misconception that there is no acceleration. "After all," they might say, "if I were driving a car in a circle at a constant speed of 20 mi/hr, then the speed is neither decreasing nor increasing; therefore there must not be an acceleration." At the

center of this common student misconception is the wrong belief that acceleration has to do with speed and not with velocity.

2. How does an object accelerate when it moves in a circle if its speed is constant?An accelerating object is an object that is changing its velocity. And since velocity

is a vector that has both magnitude and direction, a change in either the magnitude or the direction constitutes a change in the velocity. For this reason, it can be safely

concluded that an object moving in a circle at constant speed is indeed accelerating. It is accelerating because the direction of the velocity vector is changing.

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?An accelerometer is used to measure the acceleration of an object.

5. Identify three controls on an automobile that allow the car to be accelerated.The three controls that allow the car to be accelerated are the brakes, gas pedal

and steering wheel.

http://www.physicsclassroom.com/Class/1DKin/U1L1d.cfm

http://www.physicsclassroom.com/Class/1DKin/U1L1d.cfm

http://www.physicsclassroom.com/Class/1DKin/U1L1e.cfm#p2

The Centripetal Force Requirement

1. What does the word “centripetal” mean?Centripetal means center seeking.

2. Explain how inertia relates to the motion of an object traveling in a circle.According to Newton's first law of motion, it is the natural tendency of all moving objects to continue in motion in the same direction that they are moving ... unless some form of unbalanced force acts upon the object to deviate its motion from its straight-line path. Moving objects will tend to naturally travel in straight lines; an unbalanced force is only required to cause it to turn. Thus, the presence of an unbalanced force is required for objects to move in circles.

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. Friction Tension Gravity

The Forbidden F-Word

1. How does the word “centrifugal” differ from “centripetal?”Centrifugal, not to be confused with centripetal, means away from the center or outward.

2. What is a common misconception about students moving in circular motion?The common misconception, believed by many physics students, is the notion that objects in circular motion are experiencing an outward force.

3. What “law” explains the feeling of an outward force? Explain.An object moving n circular motion is at all times moving tangent to the circle; the velocity vector for the object is directedtangentially. To make the circular motion, there must be a net or unbalanced force directed towards the center of the circle in order to deviate the object from its otherwise tangential path. This path is an inward force - a centripetal force. That is spelled c-e-n-t-r-i-p-e-t-a-l, with a "p." The other word - centrifugal, with an "f" - will be considered our forbidden F-word.

http://www.physicsclassroom.com/Class/circles/u6l1a.cfm#vel

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.)

Kepler’s Three Laws

1. Who proposed the three laws of planetary motion?Johannes Kepler

2. What is Kepler’s 1st law of planetary motion?The path of the planets about the sun is elliptical in shape, with the center of the sun being located at one focus. (The Law of Ellipses)

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.An imaginary line drawn from the center of the sun to the center of the planet will sweep out equal areas in equal intervals of time. (The Law of Equal Areas)

4. What is Kepler’s 3rd law of planetary motion?The ratio of the squares of the periods of any two planets is equal to the ratio of

the cubes of their average distances from the sun. (The Law of Harmonies)

Centripetal Force (Fc)What is centripetal force?

• Some physical force pushing or pulling the object towards the center of the circle. • The word "centripetal" is merely an adjective used to describe the direction of the force. • Without the centripetal force, the object will move in a straight 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 friction acting upon the turned wheels of the car provide the

centripetal force required for circular motion.

ac

v2

R

As the moon orbits the Earth, the force of gravity 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. mass 2. Velocity 3. Radius 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 straight 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 inertia 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 tangent to the circular path along which the car is turning.

Class Work

ac

v2

R

Fc=mv2/R

Fc

v

ac

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 SolutionCentripetal force M=300 kg

R=20 mV= 3 m/s

mv2/R135 N

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

v=3 m/sR=20 m v2/R

0.45 m/s2

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?


R=3 mV= 8.1 m/s

mv2/R218.7 N

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?


R=25 mV= 12.126 m/s

mv2/R1382.17 N


v=12.126 m/sR=25 m v2/R

5.88 m/s2

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?


R=75570 mV= .25 m/s

mv2/R.000059 N


v=.25 m/sR=75570 m v2/R

.000000827 m/s2

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.


R=2.4 mV= 2.8 m/s

mv2/R81.7 N

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?


R=44 mV= 12 m/s

mv2/R212.7 N

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

v=12 m/sR=44 m v2/R

3.27 m/s2

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.


R=150 mV= 27 m/s

mv2/R5346 N

8. Roxanne is making a strawberry milkshake in her blender. A tiny, 0.0050 kg strawberry is rapidly spun around the inside container with a speed of 14.0 m/s, held by a centripetal force of 10.0 N. What is the radius of the blender at this location.

Looking For Given Relationship Solutionradius M=.005 kg

F=10 NV= 14 m/s

mv2/R.098 m

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 SolutionCentripetal force M=.4 kg

R=.8 mV= 4 m/s

mv2/R8 N

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

v=4 m/sR=.8 m v2/R

20 m/s2

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 SolutionCentripetal acceleration

v=10 m/sR=25 m v2/R

4 m/s2

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

Centripetal force M=900 kgR=25 m

V= 10 m/smv2/R

3600 N

3. According to the diagram of the plane below, the direction of the centripetal force on the airplane is directed toward: D

4. According to the diagram of the plane below, the direction of the acceleration on the airplane is directed toward: D.

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: A

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

Looking For Given Relationship SolutionAngular speed Revs = 10

Time = 5 sRevolutions/time 2 rps

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?


Time = 3 minRevolutions/time 5 rpm

(b) What is your linear speed in meters per second?Looking For Given Relationship SolutionLinear speed R=3 m

# of revs = 15Time = 180 s

2πR(# of revolutions) / time 1.57 m/s

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



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 SolutionLinear speed R=.06 m



5. A merry-go-round makes 18 rotations in 3 minutes. What is its angular speed in rpm?Looking For Given Relationship Solution

Angular speed Revs = 18Time = 3 min

Revolutions/time 6 rpm

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 SolutionLinear speed R=2 m



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


Time = 3 minRevolutions/time 4 rpm

8. Mao watches a merry-go-round as it turns 27 times in 3 minutes. The angular speed of the merry-go-round is 9 rpm.

9. Calculate the angular speed of a bicycle wheel that makes 240 rotations in 6 minutes.Looking For Given Relationship Solution



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?


Time = 3 sRevolutions/time 5 rpm

(b) What is your linear speed in meters per second?Looking For Given Relationship SolutionLinear speed R=2.5 m



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 SolutionLinear speed R=.06 m

2πR(# of revolutions) / time


.3768 m/s

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 - Northern Highlands · Web viewAn object moving in uniform circular motion is moving around the perimeter of the circle with a constant speed. While