11/03 1. which moves faster on a merry-go-round, a horse near the outside rail or one near the...

11/0311/03

1. Which moves faster 1. Which moves faster on a merry-go-round, a on a merry-go-round, a horse near the outside horse near the outside rail or one near the rail or one near the inside rail? inside rail?

2. If the hamster stops 2. If the hamster stops running does it rotate running does it rotate or does in revolve?or does in revolve?

Close reading procedureClose reading procedure

1. FIRST READ 1. FIRST READ (Key Ideas & Details)(Key Ideas & Details)

read text - Think-Pair-Share to check understanding read text - Think-Pair-Share to check understanding

2. SECOND READ 2. SECOND READ (Craft & Structure)(Craft & Structure)Number the paragraphsNumber the paragraphsCircle main vocabulary, underline main points, add question marks and exclamation Circle main vocabulary, underline main points, add question marks and exclamation Think Aloud, Shared, Paired,Think Aloud, Shared, Paired,

portions of text that will aid in citing text based evidenceportions of text that will aid in citing text based evidenceDiscuss in small and whole groupDiscuss in small and whole group

3. THIRD READ 3. THIRD READ (Integration of Knowledge and Ideas)(Integration of Knowledge and Ideas)Reread (with a group) selected chunk focusing on text dependent questionReread (with a group) selected chunk focusing on text dependent question

use pencils to mark textuse pencils to mark textfind parts of text that will aid in citing – (text based evidence)find parts of text that will aid in citing – (text based evidence)Discuss in small and whole groupDiscuss in small and whole groupJournaling with text dependent questionJournaling with text dependent question

Uniform Circular Motion and Uniform Circular Motion and Centripetal AccelerationCentripetal Acceleration

5.1 and 5.25.1 and 5.2

Centripetal force keeps an Centripetal force keeps an object in circular motion.object in circular motion.

Earth undergoes both types of rotational motion.

• It revolves around the sun once every 365 ¼ days.

• It rotates around an axis passing through its geographical poles once every 24 hours.

10.1 Rotation and Revolution

Uniform Circular MotionUniform Circular Motion

PeriodPeriod (T)(T) – Time it takes – Time it takes to make one trip around to make one trip around the circlethe circle

Circumference – Circumference – distance distance around the circlearound the circle– C = 2C = 2rr

– Object is traveling at a Object is traveling at a constant (uniform) constant (uniform) speed on a circular pathspeed on a circular path

The turntable rotates around its axis while a ladybug sitting at its edge revolves around the same axis.

10.2 Rotational Speed

Linear speed is the distance traveled per unit of time.

• Tangential speed – the linear speed of an object along a circular path

The greater distance from the axis the greater the tangential speed

Tangential and Rotational SpeedTangential and Rotational SpeedTangential speed and rotational speed are related. Tangential speed is directly proportional to the rotational speed and the radial distance from the axis of rotation.

Tangential Velocity ~ radial distance × rotational speed

Vt = r * w


In symbol form,

v ~ rwhere v is tangential speed and (pronounced oh MAY guh) is rotational speed.

• You move faster if the rate of rotation increases (bigger ).

• You also move faster if you are farther from the axis (bigger r).



Speed (v)Speed (v) – distance / time – distance / time

Find vFind v v = 3.77 m/sv = 3.77 m/s

1.2 m

T=2s


Speed is constantSpeed is constant

Velocity is not constantVelocity is not constant

Velocity is always changingVelocity is always changing

This acceleration is This acceleration is ““centripetalcentripetal”” accelerationacceleration

5.2 Centripetal Acceleration5.2 Centripetal Acceleration

Object moves in Object moves in circular pathcircular path

At time tAt time t00 it is at point it is at point

O with a velocity O with a velocity tangent to the circletangent to the circle

At time t, it is at point P At time t, it is at point P with a velocity tangent with a velocity tangent to the circleto the circle

The radius has moved The radius has moved through angle through angle

Centripetal AccelerationCentripetal Acceleration

Draw the two velocity Draw the two velocity vectors so that they vectors so that they have the same tails.have the same tails.

The vector connecting The vector connecting the heads is the heads is vv

Draw the triangle Draw the triangle made by the change in made by the change in position and you get position and you get the triangle in (b)the triangle in (b)


Since the triangles Since the triangles have the same angle have the same angle are isosceles, they are are isosceles, they are similarsimilar


Know thisKnow this

Centripetal Acceleration Centripetal Acceleration

Forces cause acceleration Forces cause acceleration F=maF=ma

AAcc = V = V22 / r centripetal acceleration / r centripetal acceleration

FFc c = m (v= m (v2 2 / r) centripetal force/ r) centripetal force

Centripetal acceleration – acceleration Centripetal acceleration – acceleration toward the centertoward the center

Centripetal force – a center directed force Centripetal force – a center directed force that causes an object to move in a curved that causes an object to move in a curved pathpath

Gravity provides constant centripetal forceGravity provides constant centripetal force

11/411/41. A 20 kg child is on the merry go round. If she is 3 m 1. A 20 kg child is on the merry go round. If she is 3 m from the center of the merry go round and her from the center of the merry go round and her tangential velocity is 2 m/s what is her centripetal tangential velocity is 2 m/s what is her centripetal acceleration? Which equation are you using?acceleration? Which equation are you using?

2. When a can is twirled in a circle, what is the 2. When a can is twirled in a circle, what is the direction of acceleration?direction of acceleration?

Today : Spinning stopper labToday : Spinning stopper lab

What are the variables that can be changed What are the variables that can be changed in the spinning stopper?in the spinning stopper?

What do you think affects the rate at which What do you think affects the rate at which the stopper spins?the stopper spins?


At any given momentAt any given moment

– vv is pointing tangent to the circle is pointing tangent to the circle

– aacc is pointing towards the center of the circle is pointing towards the center of the circle

If the object suddenly broke from circular If the object suddenly broke from circular motion would travel in line tangent to circlemotion would travel in line tangent to circle

Calculating Centripetal ForcesCalculating Centripetal ForcesGreater speed and greater mass require greater centripetal force.

Traveling in a circular path with a smaller radius of curvature requires a greater centripetal force.

Centripetal force, Fc, is measured in newtons when m is expressed in kilograms, v in

meters/second, and r in meters.

10.3 Centripetal Force

11/511/5

What two forces where acting on the What two forces where acting on the stopper allowing it to stay suspended? stopper allowing it to stay suspended?

What happens to the period (time to What happens to the period (time to complete a rotation) as your radius complete a rotation) as your radius decreases?decreases?

What can you do if you want to know if your What can you do if you want to know if your data is accurate? data is accurate?

Spinning stopper lab write upSpinning stopper lab write up Claim – how where you able to suspend the Claim – how where you able to suspend the

stopper (2 forces)stopper (2 forces)

Evidence – calulations, data table, observationsEvidence – calulations, data table, observations

Reasoning – discuss centripetal force, what was Reasoning – discuss centripetal force, what was acting on the small mass to keep it orbiting? acting on the small mass to keep it orbiting? Vocabulary : Direction, gravity, Explain Vocabulary : Direction, gravity, Explain centripetal force, centripetal acceleration in centripetal force, centripetal acceleration in terms of equations. terms of equations.

11/611/6

How many cm long is your pinky?How many cm long is your pinky?

How many meters is in 10 cm?How many meters is in 10 cm?

Due today – circular motion write upDue today – circular motion write up

See metric maniaSee metric mania Untitled – ne - Untitled – ne -

measurementmeasurement

myth busters full episodes circular motionmyth busters full episodes circular motion http://www.youtube.com/watch?v=torrlSW6Vn

A http://

www.youtube.com/watch?v=B5LCTVK8kDs&list=PL78DB5CFC40BE2225

http://www.youtube.com/watch?v=d3FrvV3It5U can you do a 360 degree swing? This claims can you do a 360 degree swing? This claims that you canthat you can

http://www.youtube.com/watch?v=torrlSW6VnA

http://www.youtube.com/watch?v=torrlSW6VnA

http://www.youtube.com/watch?v=B5LCTVK8kDs&list=PL78DB5CFC40BE2225



http://www.youtube.com/watch?v=d3FrvV3It5U

http://www.youtube.com/watch?v=d3FrvV3It5U

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

Example 1Example 1

Two identical cars are going around two Two identical cars are going around two corners at 30 m/s. Each car can handle up corners at 30 m/s. Each car can handle up to 1 g. The radius of the first curve is 50m to 1 g. The radius of the first curve is 50m and the radius of the second is 100 m. Do and the radius of the second is 100 m. Do either of the cars make the curve? (hint find either of the cars make the curve? (hint find the athe acc))

Yes, 100mYes, 100m50 m

100 m

ProblemsProblems

Try thisTry this

Concept development practice page 9-2Concept development practice page 9-2

Which arrow indicates the direction of the gravitational force the star exerts on the comet when the comet is in the position shown?

1 2 3 4

A tin can spun around on the end of a string moves in circle because

a. once the can starts moving, that is its natural tendency

b. the can continually pulls on the string c. there is a force on the can pulling

outward d. the string continually pulls inward on the

can

(8.4) Suppose a 30kg child is riding a merry go round. If she is 2.00m from the center of the merry go round and her tangential velocity is 2.50 m/s, what is her centripetal acceleration?

a. 5.00m/s2

b. 3.12m/s2

c. 281m/s2

d. 1.25m/s2

4/144/14

What determines how fast a planet revolves What determines how fast a planet revolves around the sun? mass, size, or distance around the sun? mass, size, or distance from the sun?from the sun?

How long does it take the moon to orbit the How long does it take the moon to orbit the earth? What would happen to the period if earth? What would happen to the period if the moon where farther from the earth? the moon where farther from the earth?

Due today:Stopper lab CER

Describe the motion of a satellite in relation to Earth’s surface and gravity.

14.2 Circular Orbits

A simple method of constructing an ellipse is shown here.

14.3 Elliptical Orbits

What happens if you launch a satellite at 9 km/s

Satellite speed varies in an elliptical orbit.

• When the initial speed is more than 8 km/s, the satellite overshoots a circular path and moves away from Earth.

• It loses speed due to the pull of gravity.

• The satellite slows to a point where it no longer recedes, and begins falling back toward Earth.


A satellite moves in an elliptical orbit.

a. When the satellite exceeds 8 km/s, it overshoots a circle.




b. At its maximum separation, it starts to come back toward Earth.




b. At its maximum separation, it starts to come back toward Earth.

c. The cycle repeats itself.


The parabolic paths of projectiles, such as cannonballs, are actually segments of ellipses.

a. For relatively low speeds, the center of Earth is the far focus.


The parabolic paths of projectiles, such as cannonballs, are actually segments of ellipses.

a. For relatively low speeds, the center of Earth is the far focus.

b. For greater speeds, the near focus is Earth’s center.


For a satellite in circular orbit, no force acts along the direction of motion. The speed, and thus the KE, cannot change.

14.4 Energy Conservation and Satellite Motion

think!think!The orbit of a satellite is shown in The orbit of a satellite is shown in the sketch. In which of the positions the sketch. In which of the positions A A through through D D does the satellite have does the satellite have the greatest speed? The least speed?the greatest speed? The least speed?

Answer: Answer:

The satellite has its greatest speed as it whips around The satellite has its greatest speed as it whips around A. A. It It has its least speed at has its least speed at CC. Beyond . Beyond C, C, it gains speed as it falls it gains speed as it falls back to back to A A to repeat its cycle.to repeat its cycle.


think!think!The orbit of a satellite is shown in The orbit of a satellite is shown in the sketch. In which of the positions the sketch. In which of the positions A A through through D D does the satellite have does the satellite have the greatest speed? The least speed?the greatest speed? The least speed?


What is the shape of the path of a satellite in an orbit around Earth?


Conservation of energy total energy stays Conservation of energy total energy stays the samethe same

Total energy = kinetic energy + potential Total energy = kinetic energy + potential energyenergy

Kinetic energy = energy due to speedKinetic energy = energy due to speed Potential energy = energy due to distancePotential energy = energy due to distance

• The PE is greatest when the satellite is at the apogee and least when the satellite is at the perigee.

• The KE will be least when the PE is most; and the KE will be most when the PE is least.

• At every point in the orbit, the sum of the KE and PE is constant.


For a satellite in circular orbit, no force acts along the direction of motion. The speed, and thus the KE, cannot change.


The sum of KE and PE for a satellite is a constant at all points along an elliptical orbit.


Clicker question, think!Clicker question, think!The orbital path of a satellite The orbital path of a satellite is shown in the sketch. In which is shown in the sketch. In which of the positions of the positions AA through through DD does does the satellite have the most KE? the satellite have the most KE? Most PE? Most total energy?Most PE? Most total energy?


think!think!The orbital path of a satellite The orbital path of a satellite is shown in the sketch. In which is shown in the sketch. In which of the positions of the positions AA through through DD does does the satellite have the most KE? the satellite have the most KE? Most PE? Most total energy?Most PE? Most total energy?

Answer: Answer:

The KE is maximum at The KE is maximum at A; A; the PE is maximum at the PE is maximum at C; C; the total the total energy is the same anywhere in the orbit. energy is the same anywhere in the orbit.


1. Draw a satellite in circular motion and 1. Draw a satellite in circular motion and a satellite in an elliptical orbit, what is the a satellite in an elliptical orbit, what is the difference in terms of speed and difference in terms of speed and acceleration? acceleration?

2. Why doesn't gravitational force 2. Why doesn't gravitational force change the speed of a satellite in circular change the speed of a satellite in circular motion?motion?

4/16

Ellipse – an oval where the sums of the distances from the foci to any point is constant

Ellipse – an oval where the sums of the distances from the foci to any point is constant

Eccentricity = distance between foci / length of major axis (or behavior deviating from the norm, eccentric)

d = distance between foci

L = length of major axis

E = eccentricity e = d/l

4/164/16

1.1. Which orbit has a greater eccentricity (purple or blue)?Which orbit has a greater eccentricity (purple or blue)?

2. At what point does the orbit from the blue planet have the 2. At what point does the orbit from the blue planet have the greatest kinetic energy? Potential energy? Total energy?greatest kinetic energy? Potential energy? Total energy?

Agenda - Orbital stopper lab CER (Past due)- Ellipse lab

Kepler’s 3 law =

4/174/17

Why do satellites have to be far Why do satellites have to be far above earth to keep their orbit? above earth to keep their orbit?

When is the amount of energy of a When is the amount of energy of a satellite in elliptical orbit the greatest? satellite in elliptical orbit the greatest?

Tomorrow: Quiz and notebook check dates from 4/7

1. When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it follows

a. matches the curve of planet Earth.b. results in a straight line.c. spirals out indefinitely.d. is within 150 kilometers of Earth’s surface.

Assessment Questions

1. When you toss a projectile sideways, it curves as it falls. It will be an Earth satellite if the curve it follows

a. matches the curve of planet Earth.b. results in a straight line.c. spirals out indefinitely.d. is within 150 kilometers of Earth’s surface.

Answer: A


2. When a satellite travels at constant speed, its shape is a(n)a. circle.b. ellipse.c. oval that is almost elliptical.d. square.


2. When a satellite travels at constant speed, its shape is a(n)a. circle.b. ellipse.c. oval that is almost elliptical.d. square.

Answer: A


3. A satellite in elliptical orbit about Earth travels a. fastest when it moves closer to Earth.b. fastest when it moves farther from Earth.c. slowest when it moves closer to Earth.d. at the same rate for the entire orbit.


3. A satellite in elliptical orbit about Earth travels a. fastest when it moves closer to Earth.b. fastest when it moves farther from Earth.c. slowest when it moves closer to Earth.d. at the same rate for the entire orbit.

Answer: A


4. Energy is conserved when an Earth satellite travels a. in either a circular or elliptical orbit.b. in only an elliptical orbit.c. away from Earth.d. toward Earth.


4. Energy is conserved when an Earth satellite travels a. in either a circular or elliptical orbit.b. in only an elliptical orbit.c. away from Earth.d. toward Earth.

Answer: A


5. Kepler is credited as being the first to discover that the paths of planets around the sun area. circles.b. ellipses.c. straight lines most of the time.d. spirals.


5. Kepler is credited as being the first to discover that the paths of planets around the sun area. circles.b. ellipses.c. straight lines most of the time.d. spirals.

Answer: B


http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=9

14.6 Escape Speed

Pioneer 10, launched from Earth in 1972, escaped from the solar system in 1984 and is wandering in interstellar space.

14.6 Escape Speed

4/184/18 Why is mercury the fastest moving Why is mercury the fastest moving

planet?planet?

What would happen to the length of the What would happen to the length of the month if the moon moved further out?month if the moon moved further out?

Create a diagram of the kinetic and Create a diagram of the kinetic and potential energy of a planet traveling in potential energy of a planet traveling in an ellipsean ellipse

Notebook Notebook check from 4/7check from 4/7

Due todayDue today Ellipse labEllipse lab

Test tomorrow

How does the distance between the two foci affect the eccentricity of an ellipse?

To get a lower number would you move the tacks closer or further?

Which planet was the hardest to do, why?

What remains constant for a satellite in an elliptical orbit?

What if we lost the moon?What if we lost the moon?

http://www.phy.ntnu.edu.tw/ntnujava/http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=9index.php?topic=9

http://www.youtube.com/watch?http://www.youtube.com/watch?v=DgD4nVQim-Yv=DgD4nVQim-Y

11/03 1. which moves faster on a merry-go-round, a horse near the outside rail or one near the...

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