Two Dimensional & Circular Motion
Advanced Placement Physics 1
Mr. Kuffer
1
AP Physics 1
Mr. Kuffer
A stone is thrown horizontally at a speed of +5.0 m/s from the top of a cliff 78.4 m
high.
 How long does it take the stone to reach the bottom of the cliff?
 How far from the base of the cliff does the stone strike the ground?
 What are the horizontal and vertical components of the velocity of the
stone just before it hits the ground?
2
Two Dimensional Motion
3
Projectile Motion Practice & Simulation
4
Motion in a Plane & Projectile Motion
5
Additional Projectile Problems
6
Projectile Motion
Can you get the Ball in the Cup?
Mr. Kuffer
Objective:
The purpose of this lab is to demonstrate an understanding of the independence of
vertical and horizontal velocities of a projectile by solving a problem of a projectile
launched horizontally in a lab setting.
Materials:
Ball-bearing, race-car track, stopwatch, meter stick
table, calculator, class notes, text
Styrofoam cup, lab
Setup / Procedure:
To be explained in class. If absent, be prepared to gather notes from a lab partner.
Remember to draw any diagram(s) when needed.
Horizontal launch (to take place in the classroom) – Using vx and dy
(height) of the Ball bearing, find its dx (range), vyf, and t.
Theory:
The independence of vertical and horizontal motion and our motion equations
(Use Textbook) can be used to determine the position of thrown objects. If we call the
horizontal displacement dx and the initial horizontal velocity vx then, at time t, (Note: vxf
= vxi)
dx = vxt
The equations for an object falling with constant acceleration, g, describe the
vertical motion. If dy is the vertical displacement, the initial vertical velocity of the object
is vy. At time t, the vertical displacement is
dy = vyi t + ½ gt2
Using these equations, we can analyze the motion of projectiles. (Be
sure to retain the independence of the vertical and horizontal components)
Analysis Questions:
7
1. The Ball bearing rolls “without friction” across the table at a CONSTANT
VELOCITY. When it reaches the end of the table, it flies off and lands on the
ground.
a) Draw the situation above, drawing vectors showing the Acceleration
of the Ball-bearing at two positions while it is on the table and at three
more when it is in the air. Draw all vectors to scale.
2. For the Ball bearing in question 1,
a) Draw vectors showing the horizontal and vertical components of the
Ball bearing’s velocity at the five points.
b) Using a different color, draw the total velocity vector at the five points.
3. Determine the time the ball will be in flight.
4. Determine where the ball will land.
5. What will the final velocity be in the …
a) X direction?
b) Y direction?
6. What will the total final velocity equal?
8
Projectile Problems Continued…
** Show all work on a separate sheet of paper **
9
Continued…
10
11
12
Additional Horizontal Projectile Practice Problems
9. A stone is thrown horizontally at a speed of 5.0 m/s from the top of a cliff 78.4 m high.
A) 4.0 s
B) 20 m
a. How long does it take the stone to reach the bottom of the cliff?
b. How far from the base of the cliff does the stone hit the ground?
C) Vx = 5.0 m/s
Vy = 39 m/s
c. What are the horizontal and vertical components of the
stones velocity just before it hits the ground?
10. How would the three answers to problem 9 change if…
a. The stone were thrown with twice the horizontal speed?
b. The stone were thrown with the same speed, but the cliff
were twice as high?
10 A) a) 4.0 s
b) 40 m
c) Vx = 10 m/s
Vy = 39 m/s
10 B) a) 5.7 s
b) 28 m
c) Vx = 5.0 m/s
Vy = 55 m/s
11. A steel ball rolls with constant velocity across a tabletop
0.950 m high. It rolls off and hits the ground 0.352 m from the edge of the table.
V = 0.8 m/s
How fast was the ball rolling?
13
Angular Projectile Motion
Daniel Sepulveda (now retired due to injury) punts a football at 45˚
with an initial velocity of 24 m/s.
1.
What is the hang time of the ball?
2.
What does the punt ‘net’, assuming the return man
signals for a fair catch?
3.
What was the maximum height of the punt?
Extra Practice
Solution
12) t = 2.76 s
dx = 64.6 m
dy = 9.27 m
13) t = 4.78 s
dx = 64.5 m
dy = 27.9 m
14
Ball Toss
When a juggler tosses a ball straight upward, the ball slows down until it reaches the top
of its path. The ball then speeds up on its way back down. A graph of its velocity vs. time
would show these changes. Is there a mathematical pattern to the changes in velocity?
What is the accompanying pattern to the position vs. time graph? What would the
acceleration vs. time graph look like?
In this experiment, you will use a Motion Detector to collect position, velocity, and
acceleration data for a ball thrown straight upward. Analysis of the graphs of this motion
will answer the questions asked above.
OBJECTIVES




Collect position, velocity, and acceleration data as a ball travels straight up and
down.
Analyze the position vs. time, velocity vs. time, and acceleration vs. time graphs.
Determine the best fit equations for the position vs. time and velocity vs. time
graphs.
Determine the mean acceleration from the acceleration vs. time graph.
MATERIALS
computer
Vernier computer interface
Logger Pro
Vernier Motion Detector
ball
PRELIMINARY QUESTIONS
1. Think about the changes in motion a ball will undergo as it travels straight up and
down. Make a sketch of your prediction for the position vs. time graph. Describe in
words what this graph means.
2. Make a sketch of your prediction for the velocity vs. time graph. Describe in words
what this graph means.
3. Make a sketch of your prediction for the acceleration vs. time graph. Describe in
words what this graph means.
PROCEDURE
1. Connect the Vernier Motion Detector to the DIG/SONIC 1 channel of the interface.
2. Place the Motion Detector on the table. Cover the Motion Detector with the protective
cage.
3. Open the file “06 Ball Toss” from the Physics with Computers folder.
4. In this step, you will toss the ball straight upward above the Motion Detector and let it
fall back toward the Motion Detector. This step may require some practice. Hold the
15
ball directly above and about 0.5 m from the Motion Detector. Click
to begin
data collection. You will notice a clicking sound from the Motion Detector. Wait one
second, then toss the ball straight upward. Be sure to move your hands out of the way
after you release it. A toss of 0.5 above the Motion Detector works well. You will get
best results if you catch and hold the ball when it is about 0.5 m above the Motion
Detector.
5. Examine the position vs. time graph. Repeat Step 4 if your position vs. time graph
does not show an area of smoothly changing position. Check with your teacher if you
are not sure whether you need to repeat the data collection.
ANALYSIS
1. Sketch the three motion graphs in your lab notebook. The graphs you have recorded
are fairly complex and it is important to identify different regions of each graph.
Click the Examine button, , and move the mouse across any graph to answer the
following questions. Record your answers directly on the sketched graphs.
a) Identify the region when the ball was being tossed but still in your hands:


Examine the velocity vs. time graph and identify this region. Label this on the
graph.
Examine the acceleration vs. time graph and identify the same region. Label the
graph.
b) Identify the region where the ball is in free fall:


Label the region on each graph where the ball was in free fall and moving
upward.
Label the region on each graph where the ball was in free fall and moving
downward.
c) Determine the position, velocity, and acceleration at specific points.




On the velocity vs. time graph, decide where the ball had its maximum velocity,
just as the ball was released. Mark the spot and record the value on the graph.
On the position vs. time graph, locate the maximum height of the ball during free
fall. Mark the spot and record the value on the graph.
What was the velocity of the ball at the top of its motion?
What was the acceleration of the ball at the top of its motion?
2. The motion of an object in free fall is modeled by y = v0yt + ½ gt2 (equation 6), where
y is the vertical position, v0y is the initial2 velocity in the y direction, t is time, and g is
the acceleration due to gravity (9.8 m/s ). This is a quadratic equation whose graph
is a parabola. Your graph of position vs. time should be parabolic. To fit a quadratic
equation to your data, click and drag the mouse across the portion of the position vs.
time graph that is parabolic, highlighting the free-fall portion. Click the Curve Fit
button, , select Quadratic fit from the list of models and click
. Examine the
fit of the curve to your data2and click
to return to the main graph. How closely
does the coefficient of the t term in the curve fit compare to ½ g? ( 1/2 g is 4.9…
what is ‘coefficient’? How well do they compare?)
16
3. The graph of velocity vs. time should be linear. To fit a line to this data, click and
drag the mouse across the free-fall region of the motion. Click the Linear Fit button,
. How closely does the coefficient of the t term in the fit compare to the accepted
value for g?
4. The graph of acceleration vs. time should appear to be more or less constant. Click
and drag the mouse across the free-fall section of the motion and click the Statistics
button, . How closely does the mean acceleration value compare to the values of g
found in Steps 2 and 3?
5. List some reasons why your values for the ball’s acceleration may be different from
the accepted value for g.
17
Angular
Projectile Lab
1. Label the max dy and dx.
2. Draw velocity vectors for each point of the projectile’s trajectory.
3. What is the max height of the projectile if it is launched with an initial
velocity of 4.3 m/s?
4. How long is the ball in the air?
5. What is the range of the projectile if the cart is traveling at 1.2 m/s?
HINT:
“WHAT GOES UP… MUST ____________________________...
BEFORE IT COMES BACK DOWN IT HAS GOT TO
_____________”
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Projectiles Launched at an Angle
Physics
Projectile Launcher Lab
North Allegheny SH
Mr. Kuffer
Launcher #
Names:
Period:
Determining the Range and Apex of a Projectile
Background
From class, you know that a projectile is something that is thrown or fired but not self propelled.
You also know that because of gravity pulling the projectile from its straight line path, it will
ideally follow a parabolic path. Also, you know that this seemingly complicated motion can be
simplified by looking at the two dimensions separately. Purpose
The purpose of this lab is to determine the range of a projectile launcher and the height at apex.
As a test, we will fire a plastic marble projectile through a hoop at the apex and into a container at
the maximum range.
Procedure
Step 1-Determining the initial velocity of the launcher
Using the supplied bracket, attach a photogate to the end of the projectile launcher, as shown
below.
photogate
launcher
bracket
Using gate mode, measure the time the ball will break the photogate’s beam. Prior to
loading the launcher, push the ramrod into the launcher, cocking the launcher to MEDIUM
RANGE. Shoot the launcher in a safe direction, and do not catch the ball. Record the broken
beam time below. The diameter of the ball is exactly 1 inch or .0254 m. Determine the
initial velocity of the launcher on medium range by dividing.
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distance =
0.0254
m
=
velocity=
m/sec
time =
Step 2 - Determining range of the launcher
Clamp the launcher on the end of the table. Set the launcher’s angle so that when marble is
launched on SHORT range, that it lands somewhere on the two adjacent tables.
Marble lands
somewhere on two
tables
Determine where your container should be placed to catch the marble AT THE SAME
HEIGHT IT WAS LAUNCHED by resolving your initial velocity into x- and y-components,
and then working out your horizontal and vertical mathematics.
m/sec
m/sec
m/sec
20
(X)
(Y)
acceleration = 0
acceleration = g
Try your experiment. Did it work on the first try? What are some possible sources of
error?
Continue trying and revising until you can reliably get the marble into your container.
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Step 3-Determining apex of the launcher
Obtain one of the apex hoops. Place it on a ring stand as shown below.
Calculate mathematically how high the apex ring should be so that the marble can pass
through the ring on route to the container. Show your work below.
Try your experiment. Did it work on the first try? What are some possible sources of
error?
22
Circular motion does not persist without a force
1. An overhead view of a person swinging a rock on a rope. A force from the
string is required to make the rock's velocity vector keep changing direc- tion.
2. If the string breaks, the rock will follow Newton's first law and go straight
instead of continuing around the circle.
Circular Motion
23
Angular Velocity & Centripetal Force
Vocabulary and Equations
Recall: Displacement –
Average velocity –
Average acceleration –
New Terms:
Uniform circular motion –
Axis –
Revolve –
Rotation –
Centripetal acceleration –
Period of Revolution –
Centripetal force –
Radian –
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Angular displacement –
Angular velocity –
Angular acceleration -
α=
∆𝜔
∆𝑡
Fc = mac
IMPORTANT EQUATIONS
(4π2 r)
v2
or ac =
or ac =
r
T2
ω=
2π(rad)
T
or ω =
∆θ
∆t
v = ωr
25
Example Problems – Uniform Circular Motion
1. A 150 gram ball at the end of a string is revolving uniformly in a horizontal
circle of radius 0.60 m. The ball makes 2.00 revolutions in one second.
What is its centripetal acceleration?
2. The Moon’s nearly circular orbit about the Earth has a radius of about
384,000 km and a period, T, of 27.3 days. Determine the acceleration of
the Moon toward the Earth.
3. Estimate the force a person must exert on a string attached to a 0.150 kg
ball to make the ball revolve in a horizontal circle of radius 0.6 m, as in
Example 2. The ball makes 2.00 revolutions per second. (you are unable
to solve for this problem… for now… we will talk!)
26
Practice Problems – Uniform Circular Motion
1. What is the direction of the force that acts on the clothes in the spin cycle of a
washing machine? What exerts the force?
2. Describe all the forces acting on a child riding a horse on a merry-go-round.
Which of these forces provides the centripetal acceleration of the child?
3. Will the acceleration of a car be the same when it travels around a sharp
curve at 60 km/h as when it travels around a gentle curve at the same speed?
Explain.
4. What does centripetal mean?
5. What does centrifugal mean?
Answer centripetal or centrifugal to the following statements:
6. A false force used to describe what one feels when their frame of reference is
rotating ________________.
7. Force required for any object to travel in a circular path _____________.
8. This type of force is responsible for keeping the moon in an almost perfectly
circular orbit _________________.
9. “center fleeing” _________________.
10. “center seeking” ________________.
11. How much centripetal force is required for an 850 kg race car traveling at 200
mile/hr (89.4 m/s) to go around a bend with a radius of 195 meters?
12. A runner moving at a speed of 8.8 m/s rounds a bend with a radius of 25 m.
What is the centripetal acceleration of the runner, and what exerts the
centripetal force on the runner?
13. An airplane traveling at 201 m/s makes a turn. What is the smallest radius of
the circular path (in km) the pilot can make and keep the centripetal
acceleration under 5.0 m/s2?
14. A 16 gram ball at the end of a 1.4 m string is swung in a horizontal circle. It
revolves once every 1.09 second. What is the magnitude of the string’s
tension?
27
2π radians = 360° = 1 rotation
Degrees
360
Radians
revolutions
1.5
6.28
2.5
2
180
3.14
¾
57.3
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Radians & Arc Length Lab
Objectives:
•
Students will be able to develop the relationship between radian
and arc length
•
Students will be able to demonstrate and explain why there are
2π radians in one full revolution.
•
On a separate sheet of plain white paper, use a compass to draw a
large circle.
Measure the distance from the center point to the outside of the
circle. This is the radius.
Using scissors, cut a piece of string equal to the length of the
radius
Bend the piece of string to conform to the circle, and lay the string
along the circle you drew with your compass. Tape the string in
place.
With your pencil, make a mark on the circle at each end of your
string. Draw the “piece of pie”.
Cut a new string and repeat…
• Be sure you are placing the string end to end along the arc
of the circle.
Draw lines from the center of the circle to the markings you have
just made along the circumference of the circle, *Each uniform,
large “piece of the pie” is one radian!!!
Your circle should now look kind of like a pie cut into sections.
Draw a smaller circle using your compass. Repeat all of the above
steps… starting from the same reference!!
Procedure:
•
•
•
•
•
•
•
•
Questions:
•
•
•
Approximate how many wires (of the length you cut), it would
take to outline the circumference of the circle?
Approximate how many slices of “pie” make up the entire circle?
Approximately what angle lies between each slice of “pie”?
29
ω = 2π(rad) / T
or
ω = ∆Θ / ∆t
V=ωr
Angular Velocity
1. A merry-go-round takes 6.78 seconds to make one complete turn. What was the
angular velocity?
2. If an object has an angular velocity of 0.1046 rad/sec;
a. What is its period?
b. What might the object be?
3. The angular velocity of a bicycle wheel is 50 rev/min (convert to rads/sec). A
spoke of the wheel is 50.0 cm long.
a. What is the linear velocity of a point on the tire?
b. What is the linear velocity of a point on the spoke 1/3 of the way out from
the axel?
4. A race car travels around a 1000 m radius circular track at a rate of 69.4 m/s
(250km/hr).
a. What is the car’s angular speed?
b. From a point in the center of the race track, how many degrees will the car
sweep out in ten seconds?
5. Find the angular speed and linear speed of the moon in its orbit as it makes one
revolution in 27.3 days at an average distance of 384,000,000 m from the earth.
6. What is the angular velocity of…
a. The second hand of a clock (60s)?
b. The minute hand of a clock (1hr)?
c. The hour hand of a clock (12hr)?
30
ac = v2/r
ω = 2π(rad) / T
or
ω = ∆Θ / ∆t
ac = (4π2 r)/ T2
α = Δω / Δt
OR
Angular Acceleration and
Centripetal Force
Fc = m x ac
1. The angular velocity of a bicycle wheel is 50 rev/min. Suppose the angular velocity of
the wheel increases to 100 rev/min in 10 seconds, and then comes to rest in 8.4 seconds
after that. Calculate the angular acceleration during these two periods of time.
2. What is the angular acceleration of a phonograph turntable if it reaches its angular speed
of 33 and a third rev/min in 0.25 seconds?
3. A roulette wheel turning at 1.2 rev/second comes to rest in 18.0 seconds. What was the
deceleration of the wheel?
4. A centrifuge is accelerated from an angular velocity of 3000 rev/min to 8000 rev/min in
21.5 seconds. What is its angular acceleration?
5. You enter a room and flip the switch for a ceiling fan. It takes the ceiling fan 12.3
seconds in order to be spinning at 2.35 rad/s. What was the angular acceleration of the
fan?
6. A merry-go-round is spinning at 1.65 rad/s. It is the end of the day so the operator shuts
off the power. It takes 35 s for the ride to come to a stop. What was the angular
acceleration of the ride?
7. How much centripetal force is required for an 850 kg race car traveling at 200 mile/hr
(89.4 m/s) to go around a bend with a radius of 195 meters?
8. What does centripetal mean?
9. What does centrifugal mean?
Answer centripetal or centrifugal to the following statements:
10. A false force used to describe what one feels when their frame of reference is rotating
________________.
11. Force required for any object to travel in a circular path _____________.
12. This type of force is responsible for keeping the moon in an almost perfectly circular
orbit _________________.
13. “center fleeing” _________________.
31
Centripetal Acceleration & Centripetal Force
A quick Review:
1. What are the two things needed in order for an object, any object, to travel in a
circular path?
a.
b.
2. Since an object moving in a circle is constantly changing direction, it is also
_______________
Some important Equations:
ac = v2/r
OR
&
ac = (4π2 r)/ T2
Fc = mac
1. It takes a 615 kg racing car 14.3 s to
travel at a uniform speed around a circular racetrack of 50.0 m radius.
a. Is the car accelerating?
b. What is the acceleration of the car?
c. What average force must the track exert on the tires to produce this acceleration?
2. An athlete (Idowu) whirls a 7.0kg hammer tied to the end of a 1.3 m chain in a horizontal
circle. The hammer moves at a rate of 1.0 rev/second.
a. What I the centripetal acceleration of the hammer?
b. What is the tension of the chain?
3. Kimble whirls a yo-yo in a horizontal circle. The yo-yo has a mass of 0.20 kg and is
attached to a string 0.80 m long.
a. If the yo-yo makes 1 complete revolution each second, what force does the string
exert on it?
b. Sam increases the speed of the yo-yo to 2.0 rev/sec., what force does the string
now exert?
4. According to the Guinness Book of World Records, the highest tangential speed ever
attained was 2010 m/s (4500mph). The rotating rod was 15.3 cm (0.153 m) long. Assume
the speed quoted was at the end of the rod.
a. What is the centripetal acceleration at the end of the rod?
b. What is the period of rotation of the rod, T?
5. The “Enterprise” at KENNYWOOD takes 2.4 seconds to make one revolution when it is
spinning the fastest. When you are in your seat, you are 15 m from the center.
a. What is the centripetal acceleration or the rider when the ride is spinning the
fastest?
32
Hammer throw
The modern or Olympic hammer throw is an athletic
throwing event where the object is to throw a heavy metal ball
attached to a wire and handle. The name "hammer throw" is
derived from older competitions where an actual sledge
hammer was thrown. Such competitions are still part of the
Scottish Highland Games, where the implement used is a steel
or lead weight at the end of a cane handle.
Like other throwing events, the competition is decided by who
can throw the ball the farthest. The men's hammer weighs 16
pounds (7.257 kg) and measures 3 feet 11 3⁄4 inches (121.5 cm)
in length and the women's hammer weighs 8.82 lb (4 kg) and
3 feet 11 inches (119.5 cm) in length. Competitors gain
maximum distance by swinging the hammer above their head
to set up the circular motion. Then they apply force and pick up
speed by completing one to four turns in the circle. In
competition, most throwers turn three or four times. The ball
moves in a circular path, gradually increasing in velocity with
each turn with the high point of the ball toward the sector and
the low point at the back of the circle. The thrower releases the
ball from the front of the circle. The two most important factors
for a long throw are the angle of release (45° up from the
ground) and the speed of the ball (the highest possible).
Centripetal Force Pre-Lab
1.
2.
3.
4.
5.
6.
Measure your arm length…
Determine the radius of the circle…
Determine the period (T) of the Hammer…
Calculate the angular speed (ω)…
Calculate the linear speed…
Calculate the Centripetal Force (FC)…
________________ m
________________ m
________________ s
________________ rad/s
________________ m/s
________________ N
http://www.youtube.com/watch?v=LYf8NZnh0oI
33
Centripetal Force Lab
Objective:
Name:______________
Verify the relationship between Fc, m, v , and r.
Fc = m (v2 / r)
Trial #
Mass of Stopper
(kg)
Mass of Washers
(kg)
Fc = m (9.8m/s2)
(N)
ω = 2π(rad)
Τ
ν
(ν = ω r)
1
2
3
4
5
6
7
8
9
10
11
12
Radius
(m)
Time for 20
Swings
(s)
Τ
(t/20)
(s)
(rad/s)
(m/s)
1.00
1.00
1.00
1.00
0.6
0.6
0.6
0.6
1.2
0.8
0.5
0.3
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GRAPHS: Each person will be required to create three (3) graphs from your data.
The graphs include:
#1
#2
#3
For trials 1-4 ν vs. Fc (vary Fc)
For trials 5-8 ν vs. m (vary m)
For trials 9-12 ν vs. r (vary r)
TIPS AND REMINDERS:
*** USE YOUR FLAG TO KEEP THE RADIUS CONSTANT.
THE FLAG SHOULD BE ½ INCH BELOW THE TUBE BOTTOM AT ALL
TIMES.
*** WHEN VARYING THE Fc, THE NUMBER OF WASHERS SHOULD
CHANGE BY 3 OR 4 EACH TRIAL.
*** BE CAREFUL!!!!
***YOU DO NOT HAVE TO CUT THE STRING. JUST MOVE THE FLAG
UP AND DOWN TO VARY THE RADIUS
35
Simulated Gravity:
1. Most of the energy of train systems is used in starting and stopping. The design of the
rotating train platform saves energy, because passengers can board or leave a train while
the train is still moving. Study the sketch and convince yourself that this is true. The
small circular platform in the middle is stationary, and is connected to a stationary
stairway.
a. If there is to be no relative motion between the train and the edge of the platform, how
fast must the train move compared to the rim speed of the rotating platform?
_________________________________________________________
b. Why is the stairway located at the center of the platform?
_________________________________________________________
2. The design below shows a train that makes round trips in a continuous loop from Station
A to Station B.
a. How is the size of the round platform and train speed related to the amount of time that
passengers have for boarding?
_____________________________________________________
b. Why would a rotating platform be impractical for high speed trains?
______________________________________________________________________________
____________________________________
3. Here are some people standing on a giant, rotating platform in a fun house. In the view
shown, the platform is not rotating and the people stand at rest.
36
When the platform rotates, the person in the middle stands as before. The person at the edge must
lean inward as shown. Make a sketch of the missing people to show how they must lean in
comparison.
4. The left-hand sketch below shows a stationary container of water and some floating toy
ducks. The right-hand sketch is the same container rotating about a central axis at
constant speed. Note the curved surface of the water. The duck in the center floats as
before. Make a sketch to show the orientation of the other two ducks with respect to the
water surface.
5. Consider an automobile tire half filled with water. In the cross-sectional views below, the
left- hand sketch shows the water surface when the tire is not rotating. The right-hand
sketch shows the water surface when the tire rotates about its central axis.
Now suppose the tire is rotating while in orbit in outer space. Draw the shape of the water
surface in the cross-sectional view below.
In your mind, scale up the rotating tire model to a rotating space habitat orbiting in space. If
the space habitat were half filled with water, could inhabitants float on the surface as they do
here on earth? Discuss this with your classmates.
37
AP Physics
Unit 2 Multi-Dimensional Motion
Outline
Due
Date
9/17
9/18
9/19
Topic
Class
Number
Equations of Kinematics in Two
21
Dimensions
Projectile Motion
23
24
26
27
29
Book
Assignment
Section(s)
Video(s)
3.1-3.2
2.1, 2.2, 2.3
3.3
Relative Motion
3.4
Rotational Motion and Angular
Displacement
Angular Velocity and Angular
Acceleration
Equations of Rotational Kinematics
Angular and Tangential Variables
8.1
Centripetal and Tangential
Accelerations
8.5
8.2
8.3
8.4
P:12-13, 15, 18, 20-21,
23-24, 27-28,
FOC:1, 3-4, 6
P: 30-31, 34, 36-37, 42-43,
49-51
FOC: 14-16
P:52-56, 58, 61, 63-64
FOC: 1
P: 1-2, 6-7, 11-13, 17, 19
FOC: 6
P:20, 22, 26-28, 30-31
FOC: 10-11
P:34, 36-37, 42, 44
FOC: 13-14
P:45-46, 49, 52
2.4, 2.5
2.6, 2.7
2.8
2.9
2.10-2.12
2.13, 2.14
2.15-2.17
38