Unit 06 Circular Motion Gravitation and Black Holes

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

Why don’t you fall out of a rollercoaster when it goes upside down? AAAAHHHHHHHHHHH HHHHHH!!!!

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? AAAAHHH HHHHHHH!!!!!

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: V (m/s) • Change in position • Velocity is speed and direction. • Velocity tells you “how fast” and “which way” the object moves. Acceleration: a (m/s 2) • Change in velocity • If the object is speeding up, slowing down or changing direction it is accelerating. Force: F (N) • 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)

Remember your Physics! st Newton’s 1 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

Two important key words in this unit are “Tangential” and “Centripetal”. Tangential Centripetal Tangent Straight Line Circular Circle Draw a picture representing tangential Draw a picture representing centripetal Tangential Force causes an object to… Centripetal Force causes an object to… … 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 speed of a car is constant as the car turns at 10 m/s around a corner. tangential force will cause an object to speed 2. A centripetal up or slow down. Or: 2. A centripetal force will cause an object to change direction.

Circular Motion Activity #1 Directions: • 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 group 1. 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… … a constant force has to push or pull the object inward. This force is called the centripetal force. 2. This causes the object to… …move in a circle, circular motion. It constantly changes direction! This is called centripetal acceleration. 3. When the force is no longer applied the object… … 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 Defined 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. 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. ” Tangent Line: A straight line away from a circle. With no centripetal force, an object will move tangent to it’s circular path.

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! This force is called the centripetal force. • http: //www. teachersdomain. org/asset/psu 10 phy_vid_centripetal/ Moving Marble Demonstration

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 Demo Wait a second… the water in the bucket goes in a circle because… the bucket pushes it inward? • So then… shouldn’t 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. Friction between tires and road • The Earth orbiting around the Sun. Gravity between Earth and Sun • The bucket swung in a circle (as shown). Rope attached to the bucket • Water in a bucket as the bucket is swung. The bucket pushes the water inward

Video #1 Girl Rollerblading http: //www. teachersdomain. org/resource/lsps 07. sci. phys. maf. circmotion/ 1. When no centripetal force was on the girl, which way did she move? She moved in a straight line 2. When there was a centripetal force on the girl, which way did she move? She moved in a circle 3. What provided the centripetal force? 1 st The rope 2 nd Friction

Video #2 Ball in a Circular Wall http: //www. teachersdomain. org/resource/lsps 07. sci. phys. maf. circmotion/ 1. Which way is the ball moving at the beginning of the video? In a circle. It’s circular motion. 2. To move in a circle, there must be a centripetal force on the ball, what is providing the centripetal force? The circular wall is pushing on the ball! 3. What happens to the ball’s motion when the wall is removed? The ball moves tangent! (Straight line away from the circle) 4. Why? • 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! Centripetal force In order to move in a circle, the object needs a_________. Centripetal force A ________pulls or pushes the object _____. inward Tangentially The object wants to move _____________. (in a straight line away from the circle) If the force in no longer applied, the object will move tangent from the circle because of its Inertia.

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. Rollercoaster car around a loop. The pizza dough spinning. A Jet Ski turning a corner The Earth around the sun. The car turning a corner

Video #3 Rollercoasters http: //www. teachersdomain. org/asset/phy 03_vid_roller/ http: //www. teachersdomain. org/resource/phy 03. sci. phys. mfw. roller/ As a class, watch the video on rollercoasters.

What applied a force to the rollercoaster cart as it moves upside in the loop? The track What was the direction of this force? Inward, toward the center of the circular path Draw this force on the diagram. Fc

• How did the rollercoaster cart move as a result of this force? In a circle (circular motion) • Did the rollercoaster cart (or people) fall down as it moves upside down along the track? No! • What would happen if the track suddenly disappeared when the cart was near the top of the loop? 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? The centripetal force 2. What provided the force? The rope 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 following slides are additional questions and/or examples of circular motion concepts

Video #3 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? 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? The force in inward, toward the center of the circle. a) Which way does the cup want to move? The cup wants to move tangent to the circle, in a straight line away from the circle.

Rollercoaster Questions 2. 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 Questions 3. 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 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 motion that moves an object in a circle or an arc • Circular Motion is____________________. centripetal force • For an object to move in a circle it needs a __________. tangentially • 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 _______ Centripetal force is being applied to it. The force is provided by the rope ________. If the rope broke, the bucket would move tangent, in a straight line _____________.

Centripetal Acceleration Definition • Acceleration due to a change in direction. • Centripetal acceleration is always directed toward the center of the circle (inward). Equation a c= 2 V t ------ r ac centripetal acceleration Vt tangential speed r radius

Centripetal Force Equation Definition • The force that causes circular motion. • The centripetal force is always directed toward the center of the circle, inward. F = ma a = Vt 2/r Fc = 2 m. V t ------ r F centripetal force c m mass Vt tangential speed r radius

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 10 m/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 1000 m/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 10 m/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 speed of 10 m/s. 2. A centripetal tangential force will cause an object to speed up or slow down. Or: 2. A centripetal force will cause an object to change direction.

Correct the following statements: 3. The Earth’s tangential centripetal speed around the sun is 1000 m/s. 4. The tangential centripetal acceleration of an object is caused by a change in direction. Or: 4. The tangential acceleration is caused by an object speeding up and slowing down.

Correct the following statements: 5. The object speeds up because there is a tangential centripetal force on it. Or: 5. The object changes direction because there is a centripetal force on it. 6. The velocity speed of a car is constant as the car turns at 10 m/s around a corner 7. The change in speed will cause tangential centripetal acceleration. Or: 7. A change in direction will cause centripetal acceleration.