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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?
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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
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Uniform Circular Motion and Uniform Circular Motion and Centripetal AccelerationCentripetal Acceleration
5.1 and 5.25.1 and 5.2
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Centripetal force keeps an Centripetal force keeps an object in circular motion.object in circular motion.
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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
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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
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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
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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
10.2 Rotational Speed
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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).
10.2 Rotational Speed
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Uniform Circular MotionUniform Circular Motion
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
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Uniform Circular MotionUniform Circular Motion
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
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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
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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)
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Centripetal AccelerationCentripetal Acceleration
Since the triangles Since the triangles have the same angle have the same angle are isosceles, they are are isosceles, they are similarsimilar
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Centripetal AccelerationCentripetal Acceleration
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Centripetal AccelerationCentripetal Acceleration
Know thisKnow this
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Centripetal Acceleration Centripetal Acceleration
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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
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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
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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
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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?
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Centripetal AccelerationCentripetal Acceleration
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
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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
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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?
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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.
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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
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See metric maniaSee metric mania Untitled – ne - Untitled – ne -
measurementmeasurement
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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
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http://www.youtube.com/watch?http://www.youtube.com/watch?v=PBpe_LLlQJwv=PBpe_LLlQJw
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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
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ProblemsProblems
Try thisTry this
Concept development practice page 9-2Concept development practice page 9-2
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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
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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
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(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
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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
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Describe the motion of a satellite in relation to Earth’s surface and gravity.
14.2 Circular Orbits
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A simple method of constructing an ellipse is shown here.
14.3 Elliptical Orbits
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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.
14.3 Elliptical Orbits
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A satellite moves in an elliptical orbit.
a. When the satellite exceeds 8 km/s, it overshoots a circle.
14.3 Elliptical Orbits
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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.
14.3 Elliptical Orbits
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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.
c. The cycle repeats itself.
14.3 Elliptical Orbits
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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.
14.3 Elliptical Orbits
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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.
14.3 Elliptical Orbits
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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
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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.
14.3 Elliptical Orbits
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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?
14.3 Elliptical Orbits
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What is the shape of the path of a satellite in an orbit around Earth?
14.3 Elliptical Orbits
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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
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• 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.
14.4 Energy Conservation and Satellite Motion
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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
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The sum of KE and PE for a satellite is a constant at all points along an elliptical orbit.
14.4 Energy Conservation and Satellite Motion
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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?
14.4 Energy Conservation and Satellite Motion
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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.
14.4 Energy Conservation and Satellite Motion
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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
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Ellipse – an oval where the sums of the distances from the foci to any point is constant
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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
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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 =
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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
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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
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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
Assessment Questions
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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.
Assessment Questions
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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
Assessment Questions
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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.
Assessment Questions
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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
Assessment Questions
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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.
Assessment Questions
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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
Assessment Questions
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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.
Assessment Questions
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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
Assessment Questions
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http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=9
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14.6 Escape Speed
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Pioneer 10, launched from Earth in 1972, escaped from the solar system in 1984 and is wandering in interstellar space.
14.6 Escape Speed
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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
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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?
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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