Introduction to Circular Motion Unit 06 “Circular Motion, Gravitation and Black Holes”

Introduction to Circular Motion

Unit 06“Circular Motion, Gravitation and Black

Holes”

Why don’t you fall out of a rollercoaster when it goes upside

down?

AAAAHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH!!!!

Why does pizza dough “stretches out” when you

spin it?

Why do the swings move away from the ride when it

starts?

Why do you fly off a Jet Ski when it goes around a

corner?

AAAAHHHHHHHHHHHHHHHHHHHHH!!!!!

To answer these questions … and more …

you’ll need to learn about the concepts of

Circular Motion!

Remember your math!!!

Circle

“r” radius

Circular – shaped like a circle, or motion is like a circle

Remember your Physics! Velocity:•Change in position •Velocity is speed and direction. •Velocity tells you “how fast” and “which way” the object moves.

Acceleration:•Change in velocity•If the object is speeding up, slowing down or changing direction it is accelerating.

Force: •Causes objects to accelerate.•Push or pull that makes an object speed up, slow down or change direction. •Without a net force, objects continue not moving, or moving with constant velocity. (a constant speed and direction)

V (m/s)

a (m/s2)

F (N)

an object in constant velocity motion will remain in constant velocity motion unless acted on by an outside force.”

Remember your Physics!Newton’s 1st Law

Inertia: The resistance of an object to change its motion

“An object at rest will remain at rest and an object in constant velocity motion will remain in constant velocity motion unless acted on by an outside force.”

Example:

The bus moves, but the man does not “fall

backwards”, he stays at rest

because there is no force on him.

Tangential Centripetal

Draw a picture representing tangential Draw a picture representing centripetal

Tangential Force causes an object to… Centripetal Force causes an object to…

Two important key words in this unit are “Tangential” and “Centripetal”.

Tangent Straight Line Circular Circle

… speed up or slow down(tangential acceleration)

… change direction (move in a circle, curve or arc)

(centripetal acceleration)

Time Out!Below elaborates the difference between

centripetal and tangential.

1. The velocity of a car is constant as the car turns at 10m/s around a corner.

2. A centripetal force will cause an object to speed up or slow down.

speed

tangential

Or: 2. A centripetal force will cause an object to change direction.

Circular Motion Activity #1Directions:

• In small groups use any of the material provided to make the ball move in a circle.

wiffle ball paddle string

Discuss the questions below with your group1.Draw a picture of the force showing how you

made the ball move in a circle.2. What happened to the object when you stopped

trying to make the ball move in a circle?

Class Discussion:1.To make the object move in a circle…

2.This causes the object to…

3.When the force is no longer applied the object…

… a constant force has to push or pull the object inward.This force is called the centripetal force.

…move in a circle, circular motion. It constantly changes direction!This is called centripetal acceleration.

… the object moves in a straight line away from the circle. This is called tangential motion, or moving tangent.

This is because of the object’s Inertia – with no outside force applied, the object continues to move in straight line motion!

Circular Motion is….•Motion that moves in a circle or an arc.

•Circular motion is caused by a constant inward force, objects do not move in circular motion naturally.

Examples of Circular Motion …

Circular Motion

Centripetal Force (Fc): Constant force that pushes or pulls the object inward causing circular motion.

Centripetal Acceleration (ac): Acceleration due to constant change in direction.

Circular Motion Defined

Tangent Line: A straight line away from a circle. With no centripetal force, an object will move tangent to it’s circular path.

Inertia: resistance to a change in motion“An object in constant velocity motion will remain in constant velocity motion unless acted on by an outside force.”

No object “wants” to move in a circle. The wiffle ball activity shows that in order to have circular motion

a CONSTANT inward force needs to be applied to the object!

• http://www.teachersdomain.org/asset/psu10phy_vid_centripetal/ Moving Marble Demonstration

This force is called the centripetal force.

Draw a picture of the force on the ball.

Notice!!! THERE IS NO FORCE PUSHING THE BALL OUT!!!

The only force on the ball is inward, toward the center of the circle!

Circular Motion Demonstrations

Water in Bucket DemoWait a second… the water in the bucket goes

in a circle because… the bucket pushes it inward?

• So then… shouldn’t the the water fall out of the bucket?

• There must be a force pushing the water OUTWARD so it stays in the bucket … right?

•WRONG!There is only a force pulling INWARD, not outward!

What causes the centripetal force? • A race car driving around a circular track.

• The Earth orbiting around the Sun.

• The bucket swung in a circle (as shown).

• Water in a bucket as the bucket is swung.

Friction between tires and road

Gravity between Earth and Sun

Rope attached to the bucket

The bucket pushes the water inward

Video #1 Girl Rollerbladinghttp://www.teachersdomain.org/resource/lsps07.sci.phys.maf.circmotion/

1.When no centripetal force was on the girl, which way did she move?

2. When there was a centripetal force on the girl, which way did she move?

3.What provided the centripetal force?

1st 2nd

She moved in a straight line

She moved in a circle

The rope

Friction

Video #2 Ball in a Circular Wallhttp://www.teachersdomain.org/resource/lsps07.sci.phys.maf.circmotion/

1. Which way is the ball moving at the beginning of the video?

2. To move in a circle, there must be a centripetal force on the ball, what is providing the centripetal force?

3. What happens to the ball’s motion when the wall is removed?

4. Why?

In a circle. It’s circular motion.

The circular wall is pushing on the ball!

The ball moves tangent! (Straight line away from the circle)

• Because no object wants to move in a circle. • It will only move in circular motion if there is a force on it.• When that force is not longer applied, the object will move

tangentially, or straight away from the circular path because of to its Inertia.

What Have We Learned?

No object wants to move in a circle!

In order to move in a circle, the object needs a__________________.

A ________________pulls or pushes the object _________.

The object wants to move __________________________.

If the force in no longer applied, the object will move tangentfrom the circle because of its Inertia.

Centripetal force

Centripetal force inward

Tangentially (in a straight line away from the circle)

The objects below are moving in Circular Motion.For each object below; Draw an arrow ( ) showing the direction of the force on the object. Draw an arrow ( ) showing which way the object wants to move due to its inertia.

The person on the ride moving around.

The pizza dough spinning. The Earth around the sun.

Rollercoaster car around a loop.

The car turning a corner

A Jet Ski turning a corner

Video #3 Rollercoasters

http://www.teachersdomain.org/asset/phy03_vid_roller/http://www.teachersdomain.org/resource/phy03.sci.phys.mfw.roller/

As a class, watch the video on rollercoasters.

Fc

What applied a force to the rollercoaster cart as it moves upside in the loop?

What was the direction of this force?

Draw this force on the diagram.

The track

Inward, toward the center of the circular path

• How did the rollercoaster cart move as a result of this force?

• Did the rollercoaster cart (or people) fall down as it moves upside down along the track? 

• What would happen if the track suddenly disappeared when the cart was near the top of the loop?

In a circle (circular motion)

No!

The rollercoaster cart would move tangent to the circular path – in this case upwards!

Explain “E” the key concepts• An object will only move in a circular path if a

constant inward force (the centripetal force) is applied to the object.

• Due to the object’s inertia, when this inward force is no longer applied the object will move tangent to the circular path.

• The combination of the object’s inertia (in this case the object trying to move in a straight path) and the inward force applied results in circular motion.

• If there is no centripetal force applied, the object will continue moving straight.

Circular Motion Activity : Directions:

Student volunteers make Ms Bucci and the scooter move in a circle.

Class Discussion:1.What force pulled Ms Bucci in a circle?

2.What provided the force?

3.What happened to Ms Bucci when the student let go of the rope?

She moved tangent to the circle! Moved in a straight line!This is because of her Inertia – with no force, she was able to continue moving straight.

The rope

The centripetal force

The following slides are additional questions and/or examples of circular motion concepts

Video #3 Rollercoaster Questions1. Why doesn’t the cup of water fall off the board when it is

swung in a circle?a) What is the direction of the force on the cup?

a) Which way does the cup want to move?

2. When a rollercoaster car moves in a circular loop, why don’t the people fall out of the rollercoaster car?

3. If the rollercoaster track suddenly disappeared, which way would the people and car move? Why?

Rollercoaster Questions

1. Why doesn’t the cup of water fall off the board when it is swung in a circle?a) What is the direction of the force on the cup?

a) Which way does the cup want to move?

The force in inward, toward the center of the circle.

The cup wants to move tangent to the circle, in a straight line away from the circle.

Rollercoaster Questions2. When a rollercoaster car moves in a circular loop, why

don’t the people fall out of the rollercoaster car?

• The people don’t fall out of the rollercoaster car because of their inertia.

• The people want to more in tangentially away from the track because of their inertia.

• But the centripetal force of the track pulls them inward.

• The centripetal force causes them to change their direction, so they move in a circle, around the track.

• They would never fall DOWN out of the coaster, they could only move UP because of their Inertia!!! (Tangentially away from the circle)

Rollercoaster Questions3. If the rollercoaster track suddenly disappeared,

which way would the people and car move? Why?

• If the track suddenly disappeared the people and the car would more tangentially away from the circle.

• Because of their inertia, the people and the car wanted to move tangentially away from the track– in a straight line!

• If the track is gone, the centripetal force is gone. • No centripetal force means no circular motion!

Draw a picture of the force on the ball.

Notice!!! THERE IS NO FORCE PUSHING THE BALL OUT!!!

The only force on the ball is inward, toward the center of the circle!

Wait … the water in the bucket goes in a circle because… the bucket pushes it inward?• So then… shouldn’t the the water fall out of

the bucket?• There must be a force pushing the water

OUTWARD so it stays in the bucket … right?

•WRONG!There is only a force pulling INWARD, not outward!

Review• Circular Motion is_______________________________________.

• For an object to move in a circle it needs a ___________________.

• If there is no force pulling the object, it will move______________.

Look at the picture shown.

The bucket is moving in a circle because a ______________ is being applied to it.

The force is provided by the _______________.

If the rope broke, the bucket would move _________________________.

motion that moves an object in a circle or an arc

centripetal force

tangentially

Centripetal force

rope

tangent, in a straight line

Centripetal Acceleration

EquationDefinition

•Acceleration due to a change in direction.

•Centripetal acceleration is always directed toward the center of the circle (inward).

ac

=

Vt2

-----------rac centripetal acceleration

Vt tangential speed

r radius

Centripetal Force

EquationDefinition

•The force that causes circular motion.

•The centripetal force is always directed toward the center of the circle, inward.

mVt2

-----------

rFc

=

Fc centripetal force

m mass

Vt tangential speed

r radius

F = ma a = Vt2/r

Definition

•The force that causes circular motion.

•The centripetal force is always directed toward the center of the circle, inward.

Correct the following statements:

These sentences are wrong. Change a word or phrase in each sentence so it is

correct.1. The runner turns the corner on a track with a constant velocity of 10m/s.

2. A centripetal force will cause an object to speed up or slow down.

3. The Earth’s centripetal speed around the sun is 1000m/s.

4. The tangential acceleration of an object is caused by a change in direction.

5. The object speeds up because there is a centripetal force on it.

6. The velocity of a car is constant as the car turns at 10m/s around a corner

7. The change in speed will cause centripetal acceleration.

Correct the following statements:

1. The runner turns the corner on a track with a constant velocity of 10m/s.

2. A centripetal force will cause an object to speed up or slow down.

speed

tangential

Or: 2. A centripetal force will cause an object to change direction.

Correct the following statements:

3. The Earth’s centripetal speed around the sun is 1000m/s.

4. The tangential acceleration of an object is caused by a change in direction.

tangential

Or: 4. The tangential acceleration is caused by an object speeding up and slowing down.

centripetal

Correct the following statements:

5. The object speeds up because there is a centripetal force on it.

6. The velocity of a car is constant as the car turns at 10m/s around a corner

7. The change in speed will cause centripetal acceleration.

tangential

speed

tangential

Or:5. The object changes direction because there is a centripetal force on it.

Or:7. A change in direction will cause centripetal acceleration.