Title: Introduction to Momentum
Subject: Momentum & Collisions
Class: Physics B
Grade Level: 11th and 12th
Time Required: One Shortened Period: ~ 48 Minutes
Overview: This day will serve as an introduction to the concepts of
momentum and collisions. Before moving onto collisions, students must first
be able to understand that momentum is always conserved. This lesson
focuses first on what momentum is, in terms of real life and physics definitions.
Then the focus moves towards conservation. This lesson also contains various
demonstrations to be done by the teacher and volunteers from the class.
Following the introduction to the concepts, the students will be familiarized
with the lab equipment they will be using in subsequent lessons.
Objectives: Following this introduction lesson, students will be able to define
momentum as it applies to physics, understand the meaning of conservation
applied to momentum, and be able to describe various instances where
momentum is conserved. Also, students will also be familiar with the air track
setups they will be using for future momentum and collision experiments.
Handouts/materials/resources:
 Rolling platform
 8 air track setups, with computer’s set up and ready to go
 Worksheets describing the use of computers as data collection devices
 Medicine ball
 Corrected tests from previous unit
Specific Plan:
 Begin class with a review of the previous unit test
o Go through problems that students had difficulties with
 Introduce new unit: Momentum
o Ask students for their definition of momentum
 Expect some real life examples, such as “a team has
momentum going into the playoffs”
 Compare and contrast real life vs. physics definitions
o What does it take for a bowling ball to knock over a bowling pin?
 Speed
 Mass
o
 Show demonstrations using rolling platform and medicine ball
 Show launcher on wheels demonstration with different mass projectiles
 Equation: p=mv
o Momentum=mass*velocity
o Velocity is a vector/ direction matters

Example: A 2250 kg pickup truck has a velocity of 25 m/s to the east.
What is the momentum of the truck? Ans: 56000 kg*m/s to the east
 Introduce Impulse(change in momentum) = Force*change in time
o A 1400 kg car moving westward with a velocity of 15 m/s collides
with a utility pole and is brought to rest in .3 seconds. Find the
magnitude of the force exerted on the car during the collision.
o Talk about the goals of air bags
 Discuss conservation of momentum in given systems
o Total Momentum before = total momentum after
o A 76 kg boater, initially at rest in a stationary 45 kg boat, steps
out of the boat and onto the dock. If the boater moves out of the
boat with a velocity of 2.5 m/s to the right, what is the final
velocity of the boat?
 If time, take students into lab and familiarize them with lab equipment
and setup
 Have students look through computer use worksheet and perform some
sample runs
Conclusions/assignments/assessments:
 Assign nightly homework: pg 209 # 1-4, pg 213 #1-2, pg 219 #1-4
Cautions:
 Be sure to choose volunteers who can lift and throw a medicine ball in
an appropriate manner without injuring themselves.
Title: Linear Momentum Lab
Subject: Momentum & Collisions
Class: Physics B
Grade Level: 11th and 12th
Time Required: One block period ~ 98 minutes
Overview: This lesson will largely include a lab activity that will engage the
students in an inquiry-based activity in which the students will determine the
relationship known as conservation of momentum. This lesson will also
incorporate various uses of technology in the classroom, utilizing the Pasco
Dynamics Track and Photo gates/Motion Sensors with computers. The
students will then investigate the momentum in “explosions” by determining
the mass and velocity of two carts before and after the “explosion”. This
activity also serves as a lesson in itself of using the technology, which will be
continually used throughout the unit.
Objectives: The main objective of this lesson is to have the students
understand the relationship between mass and velocity (momentum) and how
that quantity is conserved. Following the lab, students should be comfortable
with the lab equipment and the use of computers to do physics experiments.
Handouts/materials/resources:
 Copy of lab manual for each student
 8 dynamics track setups, with computer’s set up and ready to go
 Worksheets describing the use of computers as data collection devices
Specific Plan:




Begin class with a short review of lab setup
o Discuss how photo gates work
o Show students how to “wind up” carts
o Show students how to set off trigger
Pass out lab manuals and discuss write-up requirements (if not done
before then)
o Data can be left on lab worksheet, but hypothesis and analysis
should be on a separate sheet.
Have students quickly read through manual and formulate their
hypothesis. Proof of a hypothesis will be their ticket to begin their labs.
During lab, move about the room and ask open ended and thinking
questions to make sure the students are really thinking about what they
are doing.
Conclusions:

Bring students back in from lab, and quickly review their findings in the
experiment. Comment on requirements for write-up.
Cautions:

Make sure students aren’t running around in lab so they don’t knock
over the tracks
Momentum Lab: Part I
Objective: In this lab you will be investigating conservation of momentum as
it relates to objects experiencing an “explosion”. That is, the objects will be
at rest, and a force acts to cause them to move. In this case, the objects will be
the dynamics carts, and the force is supplied by the built in spring launchers
on the carts.
Materials:
2 dynamics carts with track
1 computer with LoggerPro
2 Photo gates on stands
Hypothesis: What do you think will happen when two objects of different (or
same) mass start from rest, and are then given force and putting them into
motion? Draw a graph of your prediction having three lines, one being net
momentum, one for momentum of one cart, and one for the other cart’s
momentum all vs. time. (Time on x-axis, momentum on y-axis)
Procedure:
1. Gather materials and set up LoggerPro to collect data.
a. Open LoggerPro. Then go to the file menu  open experiment
 Probes & Sensors  Photo gates  Collision Timer
b. Measure the width of the index card mounted atop the cart.
c. Open the sensors menu  setup  Data Collection  sampling
tab; change the value for the “length of object” to what you
measured the note card to be.
d. Practice with the setup to make sure it works correctly. Don’t
forget to hit the collect button.
2. Now that the sensors are working properly, place the two carts on the
track in between the photo gates (should be in the middle of the track).
Then lock the spring into place, bring the carts together, and record
the masses of each cart (each cart weights 500 grams when empty).
3. In order to set off the spring without interfering with the explosion of
the carts, use the flexible plastic ruler and quickly tap the release
switch on the cart.
4. Collect the mass and velocity of each cart and place them into the table
provided. Be sure to take the average of at least 3 trials for the sake of
accuracy.
5. Repeat these measurements with 10 different mass variations. Be sure
to have a wide range of values (using between 250 g and 1000g).
NOTE: when using heavier carts, move the photo gate closer to cart.
Data & Observations: Record your data in the provided table, and any
observations below it.
Trial
#
Mass
cart 1
Mass
cart 2
Velocity
cart 1
Velocity
cart 2
Momentum Momentum
Net
cart 1
cart 2
Momentum
m_1*v_1
m_2*v_2
(p_1 - p_2)
1
2
3
4
5
6
7
8
9
10
Analysis: Answer these questions as part of the conclusions section of your
lab write-up
1. Determine the momentum of each of the carts in your trials, and record
them into your data table.
2. What is the total momentum before and after the explosion? What
about the momentum of each individual cart?
3. Was momentum conserved in your experiments? If not, discuss
possible sources of error and how you could improve those errors in
the future.
Title: Introduce Collisions & Air Track Collisions Lab
Subject: Momentum & Collisions
Class: Physics B
Grade Level: 11th and 12th
Time Required: One block period
Overview: This lesson will build off of the previous day’s work, but add
another level of concepts. The students will now be able to piece together
what they learned in the previous day’s activity to understand the
conservation of momentum. Building off of that idea, the next logical step in
the concepts is collisions. The students will be told that there are two basic
types of collisions, elastic and inelastic. The students will only be told that
there are two types, and not what the similarities and differences are between
them. The rest will be left up to investigation using the same lab setup as the
previous day.
Objectives: Following this lesson, students will be able to understand the
application of conservation of momentum to the two forms of collisions. They
will understand that momentum is conserved in each situation, but kinetic
energy is only conserved in elastic collisions.
Handouts/materials/resources:



Copies of lab manual for each student
8 complete dynamics tracks setups with computers and cart launchers
Mass sets
Specific Plan:
 Begin class by collecting labs that were not turned in the day before
 Now that we know momentum is conserved in an explosion, what about
other events? i.e. Collisions
 Talk about three types of collisions – only talk about conservation of
momentum, leave conservation of Kinetic energy for Monday.
o Elastic - objects bounce off each other perfectly
o Inelastic - two objects move separately after collision, but make a
sound.
o Perfectly inelastic - two objects stick together after collision so
that there final velocities are the same
 Pass out lab manuals
 Introduce part II of the lab
o Same setup as before
o Demonstrate cart launcher – don’t wind up too far
o I don’t want to see carts going flying off tables
o Tell students that when they finish collecting data for their lab
and filling in all tables, start working on homework for weekend.
o Begin lab
Conclusions:
 Once each group is finished, discuss the lab report for this activity
o Details on Monday, time in class to work on it
o If students don’t finish lab, they will be able to finish next week.
 Assign homework - pg 234 22, 33, 42, 51
Cautions:



Be sure to caution students about cart launchers, DO NOT WIND THEM
UP COMPLETELY
No running around because tracks hang into aisles
Make sure too much mass isn’t being used, as that will also cause carts
to fly off of the tables
Momentum Lab: Part II
Objective: Now that you have shown that momentum is conserved in
explosions, you will investigate the same principles as they apply to collisions.
We will use the same setup as before, but this time using the cart launcher to
give the carts some initial momentum.
Materials:
2 dynamics carts with track
1 computer with LoggerPro
2 Photo gates on stands
1 cart launcher
Hypothesis: What are your predictions involving the three types of
collisions, elastic and inelastic? What quantities do you think will be
conserved?
Procedure:
1. Set up tracks, Photo Gates, and computer the same as in the previous
experiment. However, now you should remove one end bumper from
the track and replace it with a cart launcher.
2. Familiarize yourself with the cart launching mechanism. This
mechanism can be adjusted to change the launch velocity of the cart.
Do not load the launcher up completely as it will cause the carts to
fly off the track. Also at this time, figure out which end of the cart is
magnetized and which has the Velcro. You may need to exchange your
carts. Each cart should have one end Velcro and one end magnetic.
3. Now place one cart on the end of the loaded launcher, and the other
between the photo gates. Align the carts up to study perfectly inelastic
collisions (i.e. the carts will stick together after colliding). When the
computer is ready to collect data, fire the cart launcher by pulling the
yellow string. The computer will record the velocity of each cart; fill in
these values your data table. In order to figure out which masses work
best, vary both the mass being launched as well as the mass initially at
rest and decide which to use. Don’t use anything over 500 g (1 kg total
mass) on either cart.
4. Repeat this procedure for a total of 5 trials, keeping the same mass. Be
sure to write down observations of the collision itself, and not just data.
5. Now flip one of the carts around such that a magnetized side will collide
with a Velcro side. Repeat the same procedure as above, and be sure
to make note of your observations when the carts hit. Again, repeat for
a total of 5 trials.
6. Now flip the other cart around such that the magnetized ends of the
carts will repel one another. Repeat the same procedure as you did for
the inelastic collisions, but keep in mind that you may get multiple
velocities for each cart (before and after collision) so choose correctly.
If the carts actually touch you are shooting them too fast.
7. Again, perform this procedure for 5 trials.
Data & Observations: Record your data in the table, and write down any
observations below.
Inelastic Collisions: Mass Cart 1:
Run
number
Momentum
of cart 1
before
collision
Momentum
of cart 2
before
collision
1
0
2
0
3
0
4
0
5
0
Elastic Collisions:
Run
number
Momentum
of cart 1
before
collision
Momentum
of cart 1
after
collision
Momentum
of cart 2
before
collision
0
2
0
3
0
4
0
5
0
Momentum
of cart 1
after
collision
Completely Inelastic Collisions:
Momentum
of cart 1
before
collision
Momentum
of cart 2
after
collision
Total
momentum
before
collision
Mass Cart 1:
1
Run
number
Mass Cart 2:
Momentum
of cart 2
before
collision
1
0
2
0
3
0
4
0
5
0
Momentum
of cart 1
after
collision
Total
momentum
after
collision
Ratio of
total
momentum
after/befor
e
Mass Cart 2:
Momentum
of cart 2
after
collision
Total
momentum
before
collision
Mass Cart 1:
Momentum
of cart 2
after
collision
Total
momentum
before
collision
Total
momentum
after
collision
Ratio of
total
momentum
after/befor
e
Mass Cart 2:
Total
momentum
after
collision
)
Ratio of
total
momentum
after/befor
e
Analysis: Answer these questions as a part of your analysis section of your lab
write-up.
1. Determine the momentum (mv) of each cart before the collision, after
the collision, and the total momentum before and after the collision.
Calculate the ratio of the total momentum after the collision to the total
momentum before the collision. Enter the values in your data table.
2. Pick two of your trials (one elastic
and one inelastic) and determine the
kinetic energy (K.E. = ½ mv2) for each cart before and after the
collision. Calculate the ratio of the total kinetic energy after the
collision to the total kinetic energy before the collision. Show your
work.
3. If the total momentum for a system is the same before and after the
collision, we say that momentum is conserved. If momentum were
conserved, what would be the ratio of the total momentum after the
collision to the total momentum before the collision?
4. If the total kinetic energy for a system is the same before and after the
collision, we say that kinetic energy is conserved. If kinetic were
conserved, what would be the ratio of the total kinetic energy after the
collision to the total kinetic energy before the collision?
5. For your five runs, inspect the momentum ratios. Even if momentum is
conserved for a given collision, the measured values may not be
exactly the same before and after due to measurement uncertainty. The
ratio should be close to one, however. Is momentum conserved in your
collisions?
6. Repeat the preceding question for the case of kinetic energy (except
only use the trials you calculated K.E. for). Is kinetic energy conserved
in the magnetic bumper collisions? How about the Velcro collisions?
Classify the two collision types as elastic or inelastic based on what you
found in the experiment.
7. Discuss the possible reasons you may not have gotten a momentum
ratio equal to one. What were some possible sources of error? What
could you do in the future to get better data?
Title: Kinetic Energy in Collisions / lab report guidelines
Subject: Momentum & Collisions
Class: Physics B
Grade Level: 11th and 12th
Time Required: One block period
Overview: This lesson serves as an introduction (for some) to the idea of
kinetic energy as it relates to collisions. It will also serve as a collision
example day, allowing the students to work on various problems for practice.
This lesson also addresses the importance of writing a quality lab report, and
the guidelines for future lab reports.
Objectives: After this lesson, students should feel comfortable with the
calculations involved with collisions. They will also be able to understand that
kinetic energy and momentum are conserved in elastic collisions, but only
momentum is conserved in inelastic collisions. The students will also
understand what is expected of them whenever they are asked for a lab writeup.
Handouts/materials/resources:



Lab report guideline handout
Lab Analysis questions handout
Collisions practice questions handout
Specific Plan:




Begin class by checking in homework
While taking attendance, ask students to think about what kinetic
energy is. Pose question as “bell work”
Work through the homework assignment from the previous night
Using the last problem as a lead in to kinetic energy, discuss what it is
and how it could relate to the collisions we have been discussing.
o 1/2mv^2  mv
very similar, other than squared v and ½
o If kinetic energy was to be conserved, what would the collision
look/sound like?
 No sound, otherwise some of the energy would have gone
into sound.
 No heat, otherwise some of energy would have went into
heat
 Which collision looked like this?  Elastic
 Kinetic energy conserved only in elastic collisions
o Example of problem involving elastic collision
 Example problem 6G




As part of lab, calculate the K.E. in the different types of collisions to
see if it was conserved also.
Discuss details of lab
o Pass out general guide to writing lab reports
o Discuss each of the sections
o Then describe this lab in particular, what is expected.
Pass out collisions practice problems worksheet.
Allow students the rest of the class period to work on their lab writeups, or the collisions worksheet. If they work on any other class’s
homework they will get a zero for the homework.
Conclusions:


In the last five minutes, to wrap up the lesson, ask students to describe
their level of success in the labs.
o Was their momentum conserved in the collisions? If not, how
close? Which collisions gave the best conservation?
o Was kinetic energy conserved in the elastic collisions?
Anything not finished in class is to be completed as homework.
Cautions:

Make sure the students are working on their labs and/or collision
problems for homework.
Lab Report Guidelines
Anytime you are asked to do a lab write-up in physics, use these guidelines to
demonstrate your knowledge of what happened in the experiment. Each of
these sections represents what a quality lab report would contain.
Objectives: This section briefly describes the purpose of the experiment and
it would contain information about the specific concepts involved. It would
also describe the setup (i.e. equipment) used.
Hypothesis: This section would briefly describe your predictions for the
outcome of the experiment.
Procedure: This section would describe, in detail, what was actually done in
the lab. This should be written in a way that any scientist could follow your
experiment exactly as you did, and get similar results. In most cases, a
picture of the setup provides a good description of the setup.
Data & Observations: This section should consist of nice, legible data tables
with straight lines, and any observations one made during the experiment.
Also, it would include a sample calculation for each type of calculation done
(i.e. one for each section). This section would also include any graphs you
were asked to print out.
Analysis: This section would contain the answers to any lab questions asked,
as well as a paragraph summarizing what was found in the experiment. It
would also include a reflection back to your original hypothesis; was it
correct? This section would also include an analysis of the sources of error
and any improvements you would do in the future to achieve better results.
Collisions Practice
1. A 13 g bullet traveling 330 m/s penetrates a 2 kg block of wood and emerges
going 270 m/s. If the block is stationary on a frictionless surface when hit, how
fast does it move after the bullet emerges?
2. A .450 kg block, moving with a speed of 3 m/s, has a head-on collision with a .9
kg block initially at rest. Assuming a perfectly inelastic collision, what will be the
speed and direction of each block after the collision?
3. A 7.1 kg bowling ball with a speed of 6 m/s has a head on elastic collision with a
stationary 1.6 kg pin. After the collision, the ball continues forward with a
velocity of 3 m/s (a) What is the velocity of each object after the collision? (b)
What is the total momentum after the collision?
4. An eagle (m1= 4.3 kg) moving with a speed 10.2 m/s is on a head-on collision
course with a second eagle (m2 = 5.6 kg) moving at 7.8 m/s. After they collide,
they hold onto one another. In what direction and with what speed, are they
moving after the collision?
5. Two balls with masses of 2 kg and 6 kg travel toward each other at speeds of 12
m/s and 4 m/s, respectively. If the balls have a head on, inelastic collision and the
2 kg ball recoils with a speed of 8 m/s, how much kinetic energy is lost in the
collision?
6. A tennis ball of mass m = .06 kg and speed v= 25 m/s directly strikes a wall and
rebounds at the same speed. What is the impulse given the wall?
Title: Impulse and Egg Drop Activity
Subject: Momentum & Collisions
Class: Physics B
Grade Level: 11th and 12th
Time Required: One block period
Overview: This lesson serves as a fun, classical, and beneficial introduction
to the concept of impulse. After being told what impulse is, and how it is very
important in collisions (especially car crashes), the students will then be
asked to apply what they have been taught. Using the idea of impulse, the
students will design and test their own safety mechanism. The goal is to allow
an egg to be dropped from a certain height and survive the fall.
Objectives: After this lesson, students will have a better idea of how
engineers think and perform tasks. They will learn how to take a physics
concept, and a task (i.e. save an egg), and apply their creativity and
knowledge to designing a safety apparatus. Also, from this task students will
understand how cars can become safer.
Handouts/materials/resources:




4 dozen eggs
Large stack of scrap paper
Masking tape/scotch tape
Scissors
Specific Plan:






Collect homework and Labs
Go over collisions practice worksheet
Revisit idea of air bags in cars
o Why do they work? What physics do they use?
 Looking for a longer impulse, smaller force over longer
time
Introduce egg drop activity
o Groups of 3, no more or less
o Each group has 15 minutes, 5 sheets of scrap paper, and 1 meter
of tape.
o Goal: Build a contraption so that an egg doesn’t break when
dropped from various heights. ~ 1-3 meters
After 15 minutes of building, allow each group the opportunity to test
their contraption from 1 meter above plastic lined floor. Those who
survive move onto 2 meters. Any who survive that, will go to 3 meters.
Following egg drop activity, award 1 point extra credit on quiz to all
who made 3 meters.


Take the rest of class and discuss quest format, types of questions, etc.
If time, pick through sample problems in the book as examples.
Conclusions:

Remind students once again they have a quest TOMORROW.
Cautions:

Make sure to have plenty of space, eggs, plastic sheeting, and cleaning
materials on hand!
Title: Momentum & Collisions Quiz – Intro to Circular Motion
Subject: Momentum & Collisions & Circular Motion
Class: Physics B
Grade Level: 11th and 12th
Time Required: One Shortened Period: ~ 48 Minutes
Overview: This lesson will serve as a wrap-up and assessment of the first part
of the unit dealing with momentum, collisions, and impulse. By way of a
longer quiz with a variety of questions each student will demonstrate their
grasp of the material up to this point. Because this is such a long unit full of
many equations, I won’t ask the students to have a unit test with 12+ equations,
so they won’t be responsible for the math on the final unit assessment.
Following the quiz, which should take up all but around 35 minutes, I will
introduce the next section to be covered, dealing with circular motion. At this
time I will ask the students to remember earlier sections studying linear
motion. Then the linear motion will be transformed into its circular
counterparts.
Objectives: By the end of this lesson, the students will have demonstrated
their understanding of momentum and collisions, and gotten a taste of the
material that will be coming next. Following the introduction to circular
motion the students will be able to describe an aspect of linear motion, and
then relate it to its circular motion counterpart. At this point I do not expect
them to understand the math.
Handouts/materials/resources:


110 Copies of Momentum/Collisions Quiz
Momentum/Collision Quiz key
Specific Plan:
 Allow students to look over their notes, talk with peers, and ask
questions for a few minutes before quest.
 Administer quests
 Depending on how long quest takes, jump into notes on the next
section – rotational motion.
 Ask students to remember kinematics equations from first semester
o Write them on board, reiterate which variables mean what
 Now turn kinematics equations on board into a chart, labeling the
equations already present as “linear kinematics”
 Now introduce idea of rotational motion
 Quickly assess the students’ knowledge of radians as an angle measure


Have students help fill in the blanks and variables for circular motion
and label that column “rotational kinematics”
Run through sample problems from book sequentially, talking students
through each step.
Conclusion: At the end of class, call on random students and ask them what
the linear and rotational counterparts are.
Cautions: None
Momentum & Collisions Quest
1. In a perfectly inelastic collision, what is conserved?
a. Kinetic Energy
b. Momentum
c. A and B
d. None of the above
2. Airbags are an example of which of the following. Choose the best answer.
a. Momentum
b. Kinetic Energy
c. Impulse
d. Electromagnetism
3. Objects that stick together after a collision are said to have had a
_____________ collision.
a. Elastic
b. Inelastic
c. Perfectly Inelastic
d. Cozy
4. The idea that momentum before an event is equal to the momentum after
event is called __________________.
5. T or F: Kinetic energy is conserved in inelastic collisions.
6. T or F: Think of the lab where the carts started together, then sprung apart. If
one of the carts was heavier than the other, the lighter cart moved faster
because momentum was not conserved.
7. Explain why modern cars damage easily in head on collisions.
8. What are some observations one could make in a collision experiment to
decide if kinetic energy was conserved or not?
9. Describe the physics behind the contraption your group designed to protect
egg from breaking.
10. An 80 Kg running back for the University of Michigan with a speed of 13 m/s
runs into a 110 kg linebacker moving towards him at 3 m/s. Which of the
players has the greatest momentum? Which player will knock the other
backwards in a collision?
11. A 0.05 kg spit wad is traveling with a speed of 30 m/s and hits a 0.1 kg balloon
at rest. After the collision, they stick together. What is the final velocity of the
spit wad decorated balloon?
12. A 200 g bouncy ball initially travels with a speed of 18 m/s. If it bounces off of
a wall with the same speed, how much impulse does the wall provide?
13. Chuck Norris (m=75 kg) is trying to dock his canoe (15 kg). Suppose he
walks onto the dock with a velocity of 4 m/s, what velocity (include direction)
will the boat go?
14. Suppose two carts of mass 3.0 kg and 5.0 kg, moving in opposite directions,
collide with one another. Initially the carts have velocities of 6.0 m/s and 2.0
m/s respectively. In the end, the 3.0 kg cart recoils with a speed of 4 m/s and
the 5.0 kg cart moves at 3.2 m/s. How much kinetic energy is lost in the
collision?
Title: Intro to Circular Motion
Subject: Circular Motion
Class: Physics B
Grade Level: 11th and 12th
Time Required: One Block Period ~ 90 minutes
Overview: This lesson will serve as an introduction into the next section of
study, rotational/circular motion. It is mainly a lecture format with interlaced
example problems. It will also reiterate and reuse students’ prior knowledge
from first semester by way of kinematics equations.
Objectives: Following the introduction to circular motion the students will be
able to describe an aspect of linear motion, and then relate it to its circular
motion counterpart. At this point I do not expect them to understand the math.
Handouts/materials/resources: None
Specific Plan:
 Bell work problem asking students to write on a sheet of notes the
kinematics equations they remember from last semester.
 Go over quiz
 Ask students to remember kinematics equations from first semester
o Write them on board, reiterate which variables mean what
 Now turn kinematics equations on board into a chart, labeling the
equations already present as “linear kinematics”
 Now introduce idea of rotational motion
 Quickly assess the students’ knowledge of radians as an angle measure
 Angular displacement compared to linear displacement
o Sample 7a
 Angular speed compared to linear speed
o Sample 7b
 Angular acceleration compared to linear acceleration
o Sample 7C
 Have students help fill in the blanks and variables for circular motion
and label that column “rotational kinematics”
 Sample problem 7d
 Break
 How do I get from linear to rotational?
o Tangent
 Demonstrate tangent line on a circle
o Tangential speed
 Sample problem 7E
o Tangential acceleration
 Sample Problem 7F
Conclusions: At the conclusion of the lesson, call on random students to
identify the linear counterparts of circular motion. I.e. what is omega like for
linear motion?
Cautions:
 May face student resistance to do work after taking a quiz the day
before
Title: Rotational Acceleration and Forces – Force Lab
Subject: Circular Motion & Forces
Class: Physics B
Grade Level: 11th and 12th
Time Required: One shortened period + 1 block period
Overview: This lesson deals mainly with the concepts of rotational forces and
acceleration. The majority of this lesson includes teacher led lecture style
instruction. The students will be introduced to the equations dealing with
both rotational force and acceleration. After learning about the concepts, the
students will be shown the lab equipment that can be used to study centripetal
forces. They will then spend the remainder of the hour designing their own
experiment to test centripetal force.
Objectives: After this lesson, students should be able to complete a variety of
problems dealing with forces and accelerations of rotating bodies. They will
also become familiar with the force sensor and rotating force table.
Handouts/materials/resources:
 Adjustable rotating arm mechanism
 Force sensors
 Pulleys
Specific Plan:





Have homework on desk so I can go around and check it in
Go through homework assigned during previous class
Give definition of tangential
o As it relates to velocity and acceleration
Centripetal Acceleration
o Acceleration - by definition – change in velocity
 Velocity includes direction
 Acceleration = any change in direction
 What direction does velocity change to in circular motion?
 Draw figure on board
o Equation for acceleration
o Practice problem 7g #4
Centripetal Forces
o What causes objects to accelerate in a circle?
 Ask students for examples of both things that move in
circles and what makes them do so
 Cars around a turn – friction on the road
 Ball on a string – tension in the string
 Moon around the earth – gravity
 Baseball and pitchers arm – tension in arm
All examples of forces.
Forces are responsible for making an object move with
circular motion.
 What direction does the force act?
 Towards the center, just like acceleration
 We call this centripetal force
 Water bucket
 What do I notice when I’m in a car going around a turn?
 What forces do I feel?
 Force pushing away from center of circle?
 This is a fake force called centrifugal force
 Why is it a fake force?
o Your body wants to continue in a straight line
but the wall of the car gets in the way
o Due to your inertia and not a force
o Equation for centripetal force – the real one
Practice problem 7h #1
New kind of lab
o Design it yourself – design today, do lab tomorrow
o Goal: Find force on rotating body with varying angular speed
and radius.
o Materials: Rotating arm, force sensor, pulleys, string
o Write your own objectives, procedure, data tables, analysis
o For analysis, comment on how well your procedure worked,
what you would change for next time, how accurate your data
was (compare to theoretical values), and discuss possible
sources of error.
Get in groups now, and start designing your hypothesis and procedure





Conclusions:
 In the last 5 minutes get classes attention and assign homework
assignment for next class. We will finish designing the lab next class.
Homework: 255: 2
256: 2
258: 3, 5
261: 4
Cautions:
None, yet
Title: Force Lab
Subject: Momentum & Collisions
Class: Physics B
Grade Level: 11th and 12th
Time Required: One short period
Overview: This lesson will consist of an inquiry style lab that the students will
be designing themselves. This will allow them to put themselves in scientist’s
shoes, not being given a “cookie cutter” experiment where they just have to
follow the steps.
Objectives: After this lesson the students will be able to describe rotational
force and how it was determined using the lab setup. The students should
also be able to relate various equations and manipulate them for a given
variable of interest.
Handouts/materials/resources:
 110 copies of lab sheet
 Pasco rotational apparatus’
 Force sensors
 Stopwatches
 Various masses
 Power supplies
Specific Plan:
 Staple new homework and old homework together and turn in.
 Bell work: Suppose you are on the Millennium Force at Cedar Point,
going down the first drop off. At the bottom of the hill the track curves,
and resembles part of a circle with a radius of 50 meters. At the bottom
of the hill, the cart is moving at a speed of 43 m/s. What is the force felt
by the rider?
 Another roller coaster example: Suppose you are now on a roller
coaster with a loop-the-loop. How fast must the cart me moving so the
riders do not fall out while upside down (assuming they weren’t
strapped in)?
 If you were a roller coaster manufacturer, would you design it so it went
exactly that velocity?
o No, at least 1 ½ to 2 times that speed for safety reasons.
 CEDAR POINT STUFF BY END OF WEEK!!!!!!!!!!!!!!
 New kind of lab
o Design it yourself – design during first part of class, start lab
when ready
o Goal: Find force on rotating body with varying angular speed,
radius, and mass.
o Materials: Rotating apparatus, force sensor, stopwatch, etc




o Write your own procedure, data tables, and analysis
o For analysis, comment on how well your procedure worked,
what you would change for next time, how accurate your data
was (compare to theoretical values), and discuss possible
sources of error.
Get in groups now, and start designing your hypothesis and procedure
When you are done, come up to me as a group and let me approve
your procedure.
Once the group has been approved, let them begin work on their labs
Go around and make sure everyone is being safe and productive
Conclusions:
 If students finish, discuss the write-up of the lab. Turn in polished copy
of hypothesis, procedure, data, and analysis. Due the class before
spring break.
 Give warning about a test next Monday/Tuesday
o 1/3 momentum stuff
o 2/3 circular motion and centripetal forces and accelerations
o Hand out review sheet
Cautions:



Do not spin the thing too fast!
BE careful, I already hurt myself
Don’t spin with mass in track but not attached to anything….it will FLY
OFF!
Centripetal Force and Acceleration
In this lab you will design your own procedure and organize your data any
way you would like. Your goal is to get the best possible results with the least
amount of error. You must analyze the relationship between mass, velocity,
and radius as they affect the force on an object undergoing circular motion.
You will be graded on how well written your procedure is, and how well you
eliminate errors.
Recall the equation for centripetal force:
F
c

m vt
r
2
 mr 2
List of materials:
 Rotation apparatus
 Power supply
 Various masses
 Force sensor & LoggerPro
 Stopwatch
Hypothesis: What do you think will happen when you vary either m, v, or r
while keeping the others constant?
Procedure: Come up with a procedure that will allow you to single out each
of the variables in the Force equation and test each of them individually. You
will be using a stopwatch to time the apparatus, so think of ways to reduce
error in your timing (hint: we’ve done this before).
Data & Observations: Create a nice data table, either on a computer or
using a ruler, to summarize your data in a readable way. Include columns that
include all of the necessary values, one for expected theoretical values, and
one for percent error.
Analysis: First, analyze your hypothesis: was your hypothesis confirmed by
your data? Next, if you haven’t done so already, calculate your experimental
force for each of your trials. Then calculate the theoretical values for the force
of those trials. Once you have both of those values, analyze the percent error
using the same formula we used before:
Experimental  theoretical
% Error 
 100
theoretical
Finally, discuss what you would do in the future to get more accurate data, and
reduce your percent error.
Momentum & Circular Motion Test Review
Know each of these concepts by definition as well as how they are used to
solve problems:

Momentum of an object (both moving and not moving)

Impulse (both when given time, and when not given time)

Conservation of momentum as it relates to collisions and explosions

Perfectly inelastic collisions

Inelastic collisions

Elastic collisions

Angular displacement

Angular speed

Tangential speed(velocity) and tangential acceleration

Centripetal Acceleration

Centripetal Force

Centrifugal Force
Chapter 6 and 7 Equations
p  mv
Ft  p
m1v1, i  m2v2,i  m1v1, f  m2v2, f
 avg
1
K .E.  mv2
2
a t  r c
 (rad ) 
180
s
r


t
 
avg

 (deg)


t
vt  r 
vt2
ac 
 r 2
r
mvt2
Fc  2  mr 2
r
Title: Assessment of momentum and circular motion
Subject: Momentum & Collisions
Class: Physics B
Grade Level: 11th and 12th
Time Required: One block period
Overview: This lesson will serve as the summative assessment for the
momentum and circular motion unit. The range of questions will cover all
material in various fashions, utilizing multiple choice, true/false, short answer,
and calculation based problems. These problems will be taken both from
lecture material, lab material, and assigned book sections.
Objectives: During this unit, the students should demonstrate their
understanding of the material covered in the past few weeks of the course.
Handouts/materials/resources:
 110 copies of answer sheet
 31 copies of test booklet, numbered 1-31
 Test Key
Specific Plan:
 Begin class with an open floor to answer any last minute questions the
students may have about the material
 Explain answer sheet – mark answers on answer sheet ONLY, do not
write on test booklet
 Pass out tests and begin.
Conclusions:
Give students a 5 minute warning before the bell.
Cautions: None
Momentum & Circular Motion Test
Form A
DO NOT WRITE ON THIS TEST! Fill out answers on answer sheet.
p  mv
F t  p
s
 
m1v1,i  m2 v2,i  m1v1, f  m2 v2, f
r

1
 avg 
K .E.  mv 2
t
2

 (rad ) 
 (deg)
180

t
v t  r
 avg
a t  r c
vt2
 r 2
r
mvt2
Fc 
 mr 2
r
ac 
Multiple Choice: 1 point each
1. Momentum is conserved in which types of collisions?
a. Elastic
b. Inelastic
c. Perfectly Inelastic
d. All of the above
2. The units for Impulse are ______________.
a. Kg*m/s
b. Kg*m/s^2
c. N
d. 1.21 GigaWatts
3. Choose the best explanation of new car design in crashes.
a. They are built so they don’t crush in a collision, keeping the time of collision
short
b. They are built to crush easily, increasing the time of the collision and
decreasing the force
c. They are built to crush easily, decreasing the time of the collision and
decreasing the force.
4. Suppose a 60 kg bicyclist is bicycling around a park with a velocity of 10 m/s. He
abruptly strikes a tree, causing him to stop. What is his final Momentum?
a. 600 kg*m/s
b. 60 kg*m/s
c. 10 N
d. 0 kg*m/s
5. Two identical geese are traveling with the same velocity. One of the gooses hits a
telephone pole and stops in .2 seconds. The other, not paying attention to where he is
going because he is laughing so hard runs into a hot air balloon and stops in .5
seconds. Which of the geeses experiences the greater force?
a. The telephone goose
b. The hot air balloon goose
c. They experience the same force
6. Which statement correctly describes the difference between elastic and inelastic
collisions?
a. They both conserve momentum and kinetic energy.
b. They both conserve momentum, but only elastic collisions conserve kinetic
energy
c. They both conserve kinetic energy, but only inelastic collisions conserve
momentum
d. Neither conserve momentum or kinetic energy
7. If an astronaut carrying a camera becomes untethered in space (a.k.a. a vacuum) and
begins to float away from her space shuttle what can she do to get back to the ship?
a. Throw her camera at the space ship
b. Take a picture of the alien with a mullet
c. Throw her camera in the opposite direction of the ship
d. Swim towards the ship
8. During lab, as we increased the radius but kept the angular velocity constant, what
happened to the linear velocity (tangential)?
a. Increased
b. Decreased
c. Stayed the same
9. T (a) or F (b): The direction of centripetal acceleration is the same as the direction of
centripetal force.
10. If one increased the mass in the centripetal force lab while keeping the angular speed
and radius constant, how was the centripetal force affected?
a. Increased
b. Decreased
c. Stayed the same
11. Why is centrifugal force considered to be a “fake” force?
a. It’s not fake. It’s real, I’ve felt it
b. It is really just the inertia of the object in circular motion
c. It just is
12. Think about the demonstration Mr. Eldridge did in class with the water bucket.
What keeps the water in the bucket when it is upside down?
a. Gravity
b. Magic
c. The water’s inertia
d. Centripetal force
13. T (a) or F (b): When a car is going around a curve at a constant speed, it also has a
constant acceleration.
14. T (a) or F (b): Friction is always bad, and we should always take steps to eliminate it.
15. T (a) or F (b): The linear velocity of an object undergoing circular motion is always
directed towards the center of the circle.
16. If the average angular speed of Will Ferrell doing a triple axel is 40.2 rad/s, how
long would it take him to complete his maneuver (three rotations)?
a. 2.13 s
b. .402 s
c. .47 s
d. 6 days
17. When a ball is whirled in a circular motion with constant speed, which direction does
the ball accelerate?
a. Tangentially
b. Outward (away from center)
c. Inward (toward center)
d. It doesn’t accelerate
18. What is the direction of the centripetal force in the previous problem?
a. Tangentially
b. Outward (away from center)
c. Inward (toward center)
d. It has no force
19. What force keeps the Moon in a circular path around the Earth?
a. Friction
b. Centrifugal
c. Gravity
d. Tension in a giant string
20. In the centripetal force lab, if you were to increase the angular velocity by a factor of
2, how much would the force change if the mass and radius were kept constant?
a. Quadruple
b. Double
c. Triple
d. Quarter
Problems: 3 points each: You MUST show work for full points
21. Suppose you have two billiard balls on a pool table, each with a mass of .5 kg. The
first ball is moving at a speed of 4 m/s and collides elastically with a stationary ball. If
the first ball stops after the collision, how fast will the second ball go?
22. Suppose you shoot a foam Nerf ball at the back of your friend’s head with a velocity
of 15 m/s and it recoils with the same speed, what is the impulse provided by your
friend’s head?
23. A 2000 kg racecar’s tires are designed to provide a force of 40500 N to hold it
around a curve. How fast can this car go around a circular track with a radius of 100
m without slipping?
24. Jay can throw a baseball with a velocity of 135 km/hr towards home plate.
Assuming he uses a circular motion to speed up the ball and his arm is .8 m long,
what is the centripetal acceleration his arm must provide?
25. Suppose an object is attached to a string and is moving in a counter clockwise
direction in circular motion. Label the direction the object would travel if the string
was suddenly broken at point A. Draw and label the direction of the force. Draw and
label the direction of the acceleration.
A