unit 3. no talking during notes raise your hand to ask a question everyone will follow along and...

CIRCULAR MOTIONUnit 3

No talking during notes Raise your hand to ask a question Everyone will follow along and copy

into their own notes (only) Sharpen pencil when teacher is NOT

talking No one leaves during notes Be prepared to participate

Speed and Velocity

Questions Describe and give examples of circular

motion. How is the velocity of circular motion

calculated? Can you explain what direction the velocity

vectors should go during circular motion? Why?

The same concepts and ideas can be used to describe circular motion as we used to describe linear motion.

Ideas such as Newton’s laws and vectors.

Suppose that you are driving a car with the steering wheel turned so that your car followed the path of a perfect circle with a constant radius.

As you drive, you keep a constant speed of 10 mi/hr.

Your movement is called uniform circular motion.

Why is the word uniform used?

An object moving in a circle at a constant speed is one form of circular motion.

The object will cover the same distance around the circle for each segment around the perimeter of the circle.

If your car was moving in a circle at 5m/s, then each second your car moves 5 meters around the circumference.

If your car is traveling at 5 m/s, how long would it take to complete one trip around a circle with a circumference of:5 meters?15 meters?35 meters?50 meters?100 meters?

How do/did you calculate your answers?

This method to find how long it would take to travel around the circle uses the same equation used for average speed.

If needed, how do we find the circumference of a circle?

If needed, how do we find the circumference of a circle?

Circumference = 2*pi*Radius

If we combine these two equations, we can easily find a new equation to calculate the average speed of an object in uniform circular motion.

This equation shows a relationship between radius and speed.

What kind of relationship do you think this is?

Can you come up with an example to illustrate your ideas?

A string of lights? Records? Carousel?

The Velocity Vector Objects moving in uniform circular

motion have a constant speed. Can they have a constant velocity?

Explain.

Objects in uniform circular motion cannot have a constant velocity because velocity includes direction.

If an object is moving in a circular motion it cannot travel in one direction, it travels in 360 directions!

The direction is changing, so the velocity is continuously changing.Wait, that sounds familiar…. Or it should!

A change in velocity means that the object is accelerating!

We’ll go back to that in the next section.

We still need the direction for the velocities.

The speed is uniform, so the magnitude of any vector we draw will remain the same length.

The direction, though, can be shown depending on where on the circle is being discussed.

It is always a line that is tangent to the circle.

A tangent line is a line that touches a circle at one point, but does not intersect it.

I think of it as a yo-yo on a string whirling around my head and the string breaks. Where does the yo-yo go?

Questions Describe and give examples of circular

motion. How is the velocity of circular motion

calculated? Can you explain what direction the velocity

vectors should go during circular motion? Why?

Acceleration & Centripetal Force

Questions How can uniform circular motion involve

acceleration without a change in speed? What forces act on objects in circular

motion? Define centripetal. How do Newton’s laws affect circular

motion? What is the outward force that affects

objects moving in circular motion?

In the last section, we determined that objects moving in circular motion are constantly changing direction.

Given our definitions of velocity and acceleration, we determined that objects in circular motion are then always accelerating.

First, lets review acceleration.

Indicate the direction and magnitude of the acceleration for each of the following scenarios:

Now, if objects are always accelerating, they must have a direction of acceleration because acceleration is a vector.

But what is that direction?

Let’s review our vector knowledge.

The resultant is found by combining the components.

When we are looking at circular motion, what do I already know?What is the direction of my velocity?What does my resultant look like?

Given these two pieces of knowledge, can I find my acceleration vector?

What if I twirl a yo-yo on a string in a circular pattern. What direction does the force come from that keeps the yo-yo in a circle?

What keeps satellites in orbit? What direction does that force come from?

Objects moving in circular motion experience acceleration that is directed to the center of their circles.

Circular Motion Vectors

Problems

Using the circle at the right and choices above, choose the correct vector for each question.

Which vector represents the direction of the velocity at point B?

Which vector represents the acceleration at point C?Which vector represents the velocity at point C?Which vector represents the acceleration at point A?

Centripetal Force The inward force that causes acceleration

in circular motion is called centripetal force.

Centripetal means “center seeking” and describes the direction of the force.

So, objects in circular motion experience a force towards the center of their circumference.

Wait. We’ve all travelled in a circle before, or part of a circle (turning a corner).

What happened to your body when you traveled in these instances?

In order to understand the effects of centripetal forces, we also need to remember Newton’s Laws, specifically the first.

When a driver slams on the brakes in a car, what happens to your body?

What is the same driver floors the gas pedal?

Newton’s First Law

Inertia is the cause of your body moving backward and forward in those two instances.

Think about that time you were turning a corner in a car or moving in a circle.What direction did your body want to move?Why?What is causing this?

Newton’s First Law Still Applies

The inertia of your body causes your body to continue in the same direction it was traveling.

If you are the passenger you will hit the outside door, or your seatbelt will hold you in your seat.

The sensation of a force making you move outward is a false sensation.

Your body simply has inertia.

Explain the physics of these two rides.

Problem Rex Things and Doris Locked are out on a date. Rex makes a

rapid right-hand turn. Doris begins sliding across the vinyl seat (that 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 which 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.

The Forbidden F-Word What is centrifugal force?

Centrifugal means “outward” or “away from center”.

There is no such thing as a centrifugal force because objects traveling in a circle must experience a inward force.

Outward forces are caused by inertia.

This can sometimes be difficult to understand, but ask yourself:Does the sensation of moving outward

mean there was definitely an outward force?What supplies this force?Can Newton’s Laws explain the sensation?

Questions How can uniform circular motion involve

acceleration without a change in speed? What forces act on objects in circular

motion? Define centripetal. How do Newton’s laws affect circular

motion? What is the outward force that affects

objects moving in circular motion?

Gravity

Questions Explain the relationship between the

force of gravity and acceleration using Newton’s 2nd law.

What would happen to gravitational forces if the distance between objects changes?

What objects have gravity? Is there gravity in space? Explain.

Gravity and Acceleration Gravity is a force of attraction between all

objects that have mass.

Everywhere that there is mass, there is gravity.

Is there mass in space?

When a person jumps into the air, gravity causes them to slow down, come to a brief stop, and then accelerate back to the Earth.

Gravity is a force, and forces cause accelerations based on the mass of an object. (Newton’s 2nd Law)

How massive is the Earth compared to you?

Why doesn’t the Earth move to you when you jump up?

The Discovery of Gravity In the early 1600’s German astronomer

and mathematician Johannes Kepler analyzed data to describe the motion of the planets around the sun.

While Kepler’s Laws explain how the planets moved, they didn’t explain why they orbited the sun.

Isaac Newton was bothered that there was no explanation for the planets movements that also explained the moons orbit around the Earth.

What Newton did know was that there must be a centripetal force of some kind.

According to legend, at age 24 in an apple orchard, Newton was struck in the head by an apple and used this occurrence to relate the cause of the apple being drawn to the Earth as the same reason the planets are drawn to the sun.

Newton called this new notion universal gravitation.

What does universal mean?

Newton’s problem was explaining that the same gravity that pulled the apple pulled on the moon, but with less force due to distance.

The relationship between the force of gravity and the distance between objects is inversely related.

The smaller the distance between two objects, the larger the force of gravity.

The larger the distance between two objects, the smaller the force of gravity.

This is called the inverse square law.

This law will apply in other areas of physics, too.

The relationship looks like:

Using this law we can see how the forces of gravity change with the distances between objects.

Because the distance is squared, we can easily compute the changes to gravity.If the distance is doubled, the gravity is reduced

to ¼.If the distance is tripled, the gravity is reduced to

1/9.If the distance is halved, the gravity is 4 times

greater.

Questions Explain the relationship between the

force of gravity and acceleration using Newton’s 2nd law.

What would happen to gravitational forces if the distance between objects changes?

What objects have gravity? Is there gravity in space? Explain.

Kepler’s Laws

Questions Explain Kepler’s first law. Explain Kepler’s second law. Explain Kepler’s third law. At which time of year does the Earth travel

the fastest? Why? When is the Earth closest to the sun? Are

we traveling faster or slower at this point? Why?

How does this related to our use of satellites?

As stated before, in the early 1600’s Kepler used data that his mentor, Tyco Brahe, collected to fully describe the motions of the planets in a heliocentric (sun centered) solar system.

These laws are still considered to be an accurate description of planetary and satellite movement.

Kepler developed three laws to describe the motions in the solar system.The law of ellipsesThe law of equal areasThe law of harmonies

The Law of Ellipses The planets are orbiting the sun in a

path described as an ellipse.An ellipse has two foci, while a circle has

one focus.

The sun is located at one foci of the planets’ ellipses.

Draw this!

The Law of Equal Areas This law describes the speed that

planetary body move while in orbit.

The law of ellipses shows that planets are at times closer and farther away from the sun. This affects the speed at which they travel.

When do you think they travel fast/slow?

Due to the force of gravity, an orbiting object moves faster when it is closer to the sun, and slower when it is farther away.

However, if an imaginary line were drawn from the sun to the Earth, the area covered by the line would be equal for equal amounts of time.

Draw This!

Using your picture: When are we closest to the sun?

When are we traveling the fastest?

When are we traveling the slowest?

What season do we have when we are farthest from the sun?

What if we lived in the Southern Hemisphere; describe the speeds and seasons.

Law of Harmonies The 3rd law, or law of harmonies describes

the orbital period and the orbital radius.On Earth we would compare our distance from

the sun to the length of year.

The closer a planet is to the sun, the faster it travels, and the shorter it’s year.Shortest year – Mercury Longest – Neptune

Newton & Kepler Using Kepler’s Laws, Newton calculated

that the law of universal gravitation does provide the centripetal force required to keep the planets in their current orbits.

All objects orbiting another object follow these same laws.Our moonOther planets’ moonsSatellites, etc.

Satellites Satellites are categorized as either:

Natural – moons, planets, cometsMan-made – communication, weather,

scientific, intelligence, etc.

Satellites are simply projectiles.

There are satellites in circular and elliptical orbits, depending on use.

Where does the force come from to keep satellite in orbit?

Why doesn’t it fall to Earth if gravity is pulling on it?

Imagine that you are running a race. But this isn’t a normal race, you have to run circles around another person who is running in a circle.

Each time you run to pass in front of them, you would need to run a little farther. You would run a path that looked like a bunch of loop-de-loops.

This is similar to the path of satellites.

The moon orbiting the Earth, which is orbiting the sun.

Draw it! The vectors for circular and elliptical

motion.

Questions Explain Kepler’s first law. Explain Kepler’s second law. Explain Kepler’s third law. At which time of year does the Earth travel

the fastest? Why? When is the Earth closest to the sun? Are

we traveling faster or slower at this point? Why?

How does this related to our use of satellites?

unit 3. no talking during notes raise your hand to ask a question everyone will follow along and...

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