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New Vocabulary

uniform circular motion

centripetal acceleration

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Standard

HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass,�and its acceleration.

HS-PS2-4 Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.

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Learning Objective

Analyze how the apparent existence of an outward force in circular motion can be explained as inertia resisting the centripetal force.

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Success Criteria

Relate linear motion to circular motion

Find the tangential velocity

Solve problems involving centripetal acceleration.

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New Vocabulary

uniform circular motion

centripetal acceleration

centripetal force

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Review Vocabulary

average velocity: the ratio of an object’s change in position to the time interval during which the change occurred; for uniform motion, it is the slope of the object’s position-time graph

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Starter

https://www.youtube.com/watch?v=RpHVCPiPuoo

Watch the video of Ferries wheel and answer the following questions.

1. What force causses the object to move in a circular path ?

Does Ferries wheel have an acceleration ?

Think of other examples that have similar circular motion.

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Simulation

https://phet.colorado.edu/sims/cheerpj/motion-2d/latest/motion-2d.html?simulation=motion-2d

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Describing Circular Motion

Uniform circular motion is the movement of an object at constant speed around a circle with a fixed radius.
The velocity vector is always tangent to the circle.

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Centripetal Acceleration

The acceleration of an object in uniform circular motion is called center-seeking or centripetal acceleration.
Centripetal acceleration always points to the center of the circle. Its magnitude is equal �to the square of the speed, �divided by the radius of �motion.

Centripetal

Acceleration

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Practice

Calculate the orbital radius of Earth, if its tangential speed is 29.7 km/s and the centripetal acceleration acting on Earth is 5.9 × 10-3 m/s2.

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Practice

Calculate the orbital radius of Earth, if its tangential speed is 29.7 km/s and the centripetal acceleration acting on Earth is 5.9 × 10-3 m/s2.

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Quiz

It changes magnitude and is always toward the center of the circle.

It changes direction and is always tangent to the circle.

It constantly changes magnitude and direction.

It changes magnitude and is always tangent to the circle.

Which describes the velocity of an object in uniform circular motion?

CORRECT

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Quiz

It does not accelerate because it travels at a constant speed.

It accelerates because it constantly changes direction.

It does not accelerate because the force acting on it constantly changes magnitude.

It accelerates because its velocity is toward the center of a circle.

Which describes an object in uniform circular motion?

CORRECT

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Quiz

41 m/s²

4.5 m/s²

0.18 m/s²

15 m/s²

A 12.0 g rubber ball on the end of a 0.75-m string is swung in a horizontal circle. It travels at 3.4 m/s. What is the centripetal acceleration of the ball?

CORRECT

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Standard

HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass,�and its acceleration.

HS-PS2-4 Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.

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Learning Objective

Analyze how the apparent existence of an outward force in circular motion can be explained as inertia resisting the centripetal force.

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Success Criteria

Analyze the centripetal force vector

Relate circular motion with Newton’s second law

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New Vocabulary

centripetal force

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Review Vocabulary

average velocity: the ratio of an object’s change in position to the time interval during which the change occurred; for uniform motion, it is the slope of the object’s position-time graph

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Starter

Use the above simulation to find the relationship between centripetal force and …..

Velocity of the ball ?

2. Mass of the ball ?

3. Rope length ?

Create a new equation that describes the relationship among the following quantitates

https://interactives.ck12.org/simulations/physics/tetherball/app/index.html?screen=sandbox&lang=en&referrer=ck12Launcher&backUrl=https://interactives.ck12.org/simulations/physics.html

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Centripetal Acceleration

The acceleration of an object in uniform circular motion is called center-seeking or centripetal acceleration.
Centripetal acceleration always points to the center of the circle. Its magnitude is equal �to the square of the speed, �divided by the radius of �motion.

Centripetal

Acceleration

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When an object moves in a circle, the net force toward the center of the circle is called the centripetal force.
This force can be provided by any number of agents.

Centripetal Force

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Analyzing Circular Motion

Identify the agent that causes the acceleration.
Apply Newton’s second law for circular motion.

Newton’s Second Law�for Circular Motion

Centripetal Force

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Consider a ball of mass m that is being whirled in a horizontal circular path of radius r with constant speed.

Chapter 7

The force exerted by the string has horizontal and vertical components. The vertical component is equal and opposite to the gravitational force. Thus, the horizontal component is the net force.

This net force, which is is directed toward the center of the circle, is a centripetal force.

Centripetal Force

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Centripetal Force, continued

Newton’s second law can be combined with the equation for centripetal acceleration to derive an equation for centripetal force:

Chapter 7

Section 1 Circular Motion

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Practice

A pilot is flying a small plane at 56.6 m/s

in a circular path with a radius of 188.5 m. The centripetal force needed to maintain the plane’s circular motion is 1.89 × 10^4 N.

What is the plane’s mass?

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Practice

A pilot is flying a small plane at 56.6 m/s

in a circular path with a radius of 188.5 m. The centripetal force needed to maintain the plane’s circular motion is 1.89 × 10^4 N.

What is the plane’s mass?

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Classwork

1. A 2.10 m rope attaches a tire to an overhanging tree limb. A girl swinging on the

tire has a tangential speed of 2.50 m/s. If the magnitude of the centripetal force is

88.0 N, what is the girl’s mass?

2. A bicyclist is riding at a tangential speed of 13.2 m/s around a circular track.

The magnitude of the centripetal force is 377 N, and the combined mass of

the bicycle and rider is 86.5 kg. What is the track’s radius?

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Classwork A.K

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Standard

HS-PS2-1. Analyze data to support the claim that Newton’s second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass,�and its acceleration.

HS-PS2-4 Use mathematical representations of Newton’s Law of Gravitation and Coulomb’s Law to describe and predict the gravitational and electrostatic forces between objects.

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New Vocabulary

Centrifugal force

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Starter

Search in google or YouTube about ( Centrifugal force )

Have a class discussion about the topic using the following questions

1- What is centrifugal force ?

2- Give real life application about it.

3- Mention 3 forces can be considered as centripetal force

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Practice

A roller coaster’s passengers are suspended upside down as it moves at a constant speed through a vertical loop. What is the direction of the force that causes the coaster and its passengers to move in a circle? What provides this force?