Download Uniform Circular Motion and Centripetal Acceleration

11/03
1. Which moves faster
on a merry-go-round, a
horse near the outside
rail or one near the
inside rail?
2. If the hamster stops
running does it rotate
or does in revolve?
Close reading procedure
1. FIRST READ (Key Ideas & Details)
 read text - Think-Pair-Share to check understanding
2. SECOND READ (Craft & Structure)
 Number the paragraphs
 Circle main vocabulary, underline main points, add question marks
and exclamation
 Think Aloud, Shared, Paired,
portions of text that will aid in citing text based evidence
 Discuss in small and whole group
3. THIRD READ (Integration of Knowledge and Ideas)
 Reread (with a group) selected chunk focusing on text dependent
question
use pencils to mark text
 find parts of text that will aid in citing – (text based evidence)
5.1 and 5.2
Uniform Circular Motion and
Centripetal Acceleration
Centripetal force keeps an
object in circular motion.
10.1 Rotation and Revolution
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.
Uniform Circular Motion
 Period (T) – Time it takes
to make one trip around
the circle
 Circumference – distance
around the circle
– C = 2r
– Object is traveling at a
constant (uniform)
speed on a circular path
10.2 Rotational Speed
The turntable rotates around its axis while a ladybug sitting at its edge revolves
around the same axis.
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
10.2 Rotational Speed
Tangential and Rotational Speed
Tangential 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
In symbol form,
v ~ r
where 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).
Uniform Circular Motion
 Speed (v) – distance / time
1.2 m
 Find v
 v = 3.77 m/s
T=2s
Uniform Circular Motion
 Speed is constant
 Velocity is not constant
 Velocity is always changing
 This acceleration is “centripetal”
acceleration
5.2 Centripetal Acceleration
 Object moves in
circular path
 At time t0 it is at point
O with a velocity
tangent to the circle
 At time t, it is at point P
with a velocity tangent
to the circle
 The radius has moved
through angle 
Centripetal Acceleration
 Draw the two velocity
vectors so that they
have the same tails.
 The vector connecting
the heads is v
 Draw the triangle
made by the change in
position and you get
the triangle in (b)
Centripetal Acceleration
 Since the triangles
have the same angle
are isosceles, they are
similar
Centripetal Acceleration
Centripetal Acceleration
Know this
Centripetal Acceleration
 Forces cause acceleration
 F=ma
 Ac = V2 / r
 Fc = m (v2 / r)
centripetal acceleration
centripetal force
 Centripetal acceleration – acceleration
toward the center
 Centripetal force – a center directed force
that causes an object to move in a curved
path
 Gravity provides constant centripetal force
11/4
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 tangential velocity is 2 m/s what
is her centripetal acceleration? Which
equation are you using?
2. When a can is twirled in a circle, what is the
direction of acceleration?
Today : Spinning stopper lab
 What are the variables that can be changed
in the spinning stopper?
 What do you think affects the rate at which
the stopper spins?
Centripetal Acceleration
 At any given moment
– v is pointing tangent to the circle
– ac is pointing towards the center of the circle
 If the object suddenly broke from circular
motion would travel in line tangent to circle
10.3 Centripetal Force
Calculating Centripetal Forces
Greater 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.
11/5
 What two forces where acting on the
stopper allowing it to stay suspended?
 What happens to the period (time to
complete a rotation) as your radius
decreases?
 What can you do if you want to know if
your data is accurate?
Spinning stopper lab write up
 Claim – how where you able to suspend
the stopper (2 forces)
 Evidence – calulations, data table,
observations
 Reasoning – discuss centripetal force,
what was acting on the small mass to keep
it orbiting? Vocabulary : Direction, gravity,
Explain centripetal force, centripetal
acceleration in terms of equations.
11/6
 How many cm long is your pinky?
 How many meters is in 10 cm?
Due today – circular motion write up
 See metric mania
 Untitled – ne measurement
 myth busters full episodes circular motion
 http://www.youtube.com/watch?v=torrlSW6Vn
A
 http://www.youtube.com/watch?v=B5LCTVK8
kDs&list=PL78DB5CFC40BE2225
 http://www.youtube.com/watch?v=d3FrvV3It5
U can you do a 360 degree swing? This
claims that you can
 http://www.youtube.com/watch?v=PBpe_L
LlQJw
Example 1
 Two identical cars are going around two
corners at 30 m/s. Each car can handle up
to 1 g. The radius of the first curve is 50m
and the radius of the second is 100 m. Do
either of the cars make the curve? (hint find
the ac)
 Yes, 100m
50 m
100 m
Problems
 Try this
 Concept 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
Due today:
Stopper lab
CER
4/14
 What determines how fast a planet revolves
around the sun? mass, size, or distance
from the sun?
 How long does it take the moon to orbit the
earth? What would happen to the period if
the moon where farther from the earth?
14.2 Circular Orbits
Describe the motion of a satellite in relation to Earth’s surface
and gravity.
14.3 Elliptical 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.
14.3 Elliptical Orbits
A satellite moves in an elliptical orbit.
a. When the satellite exceeds 8 km/s, it overshoots a circle.
14.3 Elliptical Orbits
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
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
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
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.
14.4 Energy Conservation and Satellite Motion
For a satellite in circular orbit, no force acts along the direction of motion.
The speed, and thus the KE, cannot change.
14.3 Elliptical Orbits
think!
The orbit of a satellite is shown in
the sketch. In which of the positions
A through D does the satellite have
the greatest speed? The least speed?
Answer:
The satellite has its greatest speed as it whips around A. It
has its least speed at C. Beyond C, it gains speed as it falls
back to A to repeat its cycle.
14.3 Elliptical Orbits
think!
The orbit of a satellite is shown in
the sketch. In which of the positions
A through D does the satellite have
the greatest speed? The least speed?
14.3 Elliptical Orbits
What is the shape of the path of a satellite in an orbit around
Earth?
 Conservation of energy total energy stays
the same
 Total energy = kinetic energy + potential
energy
 Kinetic energy = energy due to speed
 Potential energy = energy due to distance
14.4 Energy Conservation and Satellite Motion
• 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
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
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
Clicker question, think!
The orbital path of a satellite
is shown in the sketch. In which
of the positions A through D does
the satellite have the most KE?
Most PE? Most total energy?
14.4 Energy Conservation and Satellite Motion
think!
The orbital path of a satellite
is shown in the sketch. In which
of the positions A through D does
the satellite have the most KE?
Most PE? Most total energy?
Answer:
The KE is maximum at A; the PE is maximum at C; the total
energy is the same anywhere in the orbit.
4/16
 1. Draw a satellite in circular motion and
a satellite in an elliptical orbit, what is the
difference in terms of speed and
acceleration?
 2. Why doesn't gravitational force
change the speed of a satellite in circular
motion?
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
4/16
Agenda
- Orbital stopper lab CER (Past
due)
- Ellipse lab
Kepler’s 3 law =
1.
Which orbit has a greater eccentricity (purple or blue)?
2. At what point does the orbit from the blue planet have the
greatest kinetic energy? Potential energy? Total energy?
4/17
 Why do satellites have to be far
above earth to keep their orbit?
 When is the amount of energy of a
satellite in elliptical orbit the greatest?
Tomorrow: Quiz and
notebook check dates
from 4/7
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.
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
Assessment Questions
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
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
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
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
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
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
5.
Kepler is credited as being the first to discover that the paths of
planets around the sun are
a. circles.
b. ellipses.
c. straight lines most of the time.
d. spirals.
Assessment Questions
5.
Kepler is credited as being the first to discover that the paths of
planets around the sun are
a. 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
14.6 Escape Speed
Pioneer 10, launched from Earth in 1972, escaped from the solar system in
1984 and is wandering in interstellar space.
4/18
 Why is mercury the fastest moving
planet?



Notebook check
from 4/7
Due today
Ellipse lab
 What would happen to the length of the
month if the moon moved further out?
 Create a diagram of the kinetic and
potential energy of a planet traveling in
an ellipse
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?
 http://www.phy.ntnu.edu.tw/ntnujava/index.p
hp?topic=9
 http://www.youtube.com/watch?v=DgD4nV
Qim-Y