7.3 Circular Motion and Gravitypp. 260 - 265

Mr. Richter

Agenda

Warm-Up

Intro to rotational motion.

Refresh on Newton’s Laws

Notes: Centripetal Force Centripetal Force and Inertia Circular motion The Myth of Centrifugal Force

Objectives: We Will Be Able To…

Explain how a centripetal force causes circular motion

List the factors that affect centripetal force

Describe the relationship between gravitational force, mass, and distance

Relate centripetal force to orbital motion

Warm-Up:

Centripetal Force

Centripetal Force

Usually we think of a force as changing the speed of an object.

But what else can forces do?

Centripetal force is any force that is applied that changes the direction of an object but not its speed.

Centripetal Force

Centripetal force is applied perpendicular to the motion of an object.

It causes the object to move in a circular path.

Centripetal force always points toward the center of the circle.

Centripetal Force

Velocity

Centripetal

Force

Centripetal Force and Inertia

Why doesn’t the ball get pulled in to the center?

Why doesn’t the ball go rocketing off in some direction?

Answer: the ball has inertia to keep going the same speed if the

force doesn’t speed it up or slow it down, and the force is perpendicular to motion, so it only changes

the ball’s direction toward the middle of the circle

Centripetal Force and Inertia

Force and velocity are always perpendicular to each other.

If the string is suddenly cut (or if Mr. Richter lets go), then the ball will continue in a straight-line path at a 90° angle from the string.

Warm-Up

A boy swings a ball in a circle on a string above his head. What factors do you think will make a difference in how much centripetal force he has to apply to keep the ball spinning in a circle?

Think and then discuss at your table. We will discuss as a class in a few minutes.

Centripetal Force Video

http://www.youtube.com/watch?v=PBpe_LLlQJw

Circular Motion

Circular Motion

How does the centripetal force change with the radius of the circle?

As the radius increases, the object turns more gradually, so the force required to turn the object is less. Force is inversely proportional to radius.

How does the centripetal force change with the mass of the object?

As the mass of the object increases, more force is required to cause it to turn. Force is directly proportional to mass.

Circular Motion

How does the centripetal force change with the speed of the object?

As the speed of an object increases, the amount of force required to turn the object increases. Force is directly proportional to the square of the speed.

Meaning: twice as fast means four times the force required three times as fast means nine times the force

Warm-Up

If the radius of an object’s orbit is doubled, by what factor does the centripetal force increase or decrease?

If the speed of an object’s orbit is quadrupled, by what factor does the centripetal force increase or decrease?

The Myth of Centrifugal Force

The Rotor Ride

http://www.youtube.com/watch?v=Or0IFpRSTjM

The Rotor Ride

Explain what you think is happening on the rotor ride you saw. Is there really a force coming from the middle of the ride, pushing people against the wall? If not, what do you think is really happening?

Discuss at your table and we will discuss in a few minutes.

The Myth of “Centrifugal Force”

It might seem like as an object is rotating, there is a force pushing the object away from the center of the circle.

THIS IS NOT TRUE. THERE IS NO SUCH THING AS CENTRIFUGAL FORCE! There is no force pushing away from the center of the circle.

Objects just want to keep going in a straight line. Inertia, not force.

Gravitational ForceDoes the moon pull on the earth?

Gravitational Force Newton observed that some

centripetal force must be required to cause planets and moons to orbit in a circle.

He determined that this force must be gravity!

Gravity is a form of centripetal force!

The force of gravity between two objects is the same in both directions. The moon pulls on Earth the same

as Earth pulls on the moon.

Gravitational Force

Gravitational force exists between ALL objects that have mass.

Your weight is the force of gravity between you and the Earth. This force changes if you travel to another planet, get

farther from the earth, or go to the moon.

It takes an enormous amount of mass to have a noticeable force of gravity.

Gravitational Force

The gravitational force between two objects always lies along the line connecting their centers.

The size of the force depends on:

The mass of each object: as masses increase, the force of gravity increases.

The distance between the objects from center to center: force decreases with the square of the distance.

Think About It

According to the Law of Universal Gravitation formula, will you weigh more or less (or the same) on the top of Mt. Everest?

Note: Measuring Distance

We measure distance between two objects from their centers:

NOT because gravity comes from the center of objects. ALL of the object’s mass contributes to the force of gravity.

The center is your average distance to all parts of the object.

Calculating the Force of Gravity Newton’s Law of Universal

Gravitation gives the relationship between gravitational force, distance, and the masses of any two objects.

G is the gravitational constant: 6.67 x 10-11 Nm2/kg2

Note: because G is so small, at least one mass needs to be very large to have much gravitational force.

Your Turn

Use the following information to calculate the force of gravity between Earth and the moon. Mass of Earth: 5.97 × 1024 kg Mass of moon: 7.34 × 1022 kg Distance between centers of Earth and moon: 3.84×108 m

Answer: 1.99 x 1020 N

Practice

Calculate the force between two objects that have masses of 70 kilograms and 2,000 kilograms separated by a distance of 1 meter.

A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 x 106 meters. Find the mass of the moon.

Wrap-Up: Did we meet our objectives?

Explain how a centripetal force causes circular motion

List the factors that affect centripetal force

Describe the relationship between gravitational force, mass, and distance

Relate centripetal force to orbital motion

Homework

Due Monday

p265 Gravitational Force #1-3

p265 Section Review #1, 3

p 270 #34, 36

Boooooks!