Download Unit 6: Circular Motion and Torque

Unit 6: Circular Motion and Torque
Lesson 1 - Circular Motion
READ Chapter 9 Take NOTES
Concept Development 9-2
Problems Solving 6-1
1.1
Web Walk - Understanding and Applying Circular Motion
1.2
Lab Activity – Going In Circles In class
1.3
Online Problem Solving
1.4
Quiz – Circular Motion
Lesson 2 - Center of Gravity
READ 10 Take NOTES
Concept Development 10-1
Problems Solving 6-2
2.1
Lab Activity - Center of Gravity
2.2
Practice Online Quiz - Center of Gravity
2.3
Center of Gravity Demonstrations and Review
2.4
Quiz – Center of Gravity
Lesson 3 - Rotational Mechanics
READ Chapter 11 Take NOTES
Concept Development 11-1 and 11-2
Problems Solving 6-3
3.1
Virtual Lab – Torque
3.2
Lab Activity – Rotational Derby
3.3
Online Concept/Problem Review
3.4
Lesson Wrap Up – Physics Thoughts for Discussion
3.5
Knowledge Check
Lesson 4 - Unit Assessment
 Review Data sheet
 Take unit test
By the end of this unit, you will be able to:
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distinguish between rotate and revolve
distinguish between linear and rotational speed
describe the velocity of an object moving in uniform circular motion at any point
in that motion
demonstrate that the acceleration of an object may result in a change in direction
with no change in speed
define centripetal acceleration
define centripetal force
explain why centrifugal force is “fictitious”
solve problems involving:
centripetal force, centripetal acceleration, speed, radius of revolution, period of
revolution, object's mass
analyze and describe the forces acting on common objects in circular motion
define center of gravity , give examples of how center of gravity affects objects
and people, and describe how to find its location of irregularly shaped objects
distinguish between stable, unstable, and neutral equilibrium
define torque and identify situations involving the application of torque
solve problems involving:
torque, force, lever arm
define angular velocity
define angular acceleration
define angular momentum and describe the conditions under which it changes and
remains the same
define rotational inertia and describe what rotational inertia depends on
Our scenario for this unit will be to apply the kinematics concepts and motion principles
will be to the motion of objects in circles and then extended to analyze the motion of such
objects as roller coaster cars, a football player making a circular turn, and a planet
orbiting the sun. We will see that the beauty and power of physics lies in the fact that a
few simple concepts and principles can be used to explain the mechanics of everyday
situations.
When riding an amusement park ride, you feel as if a force is pushing you against the
side or pulling you in a direction away from the center. This is commonly called
“centrifugal force” (a fictitious force), however; it is actually the result of inertia that
causes you to maintain the motion in a straight line path. The effects of this “fictitious
force” are everywhere. For example, when you punch the accelerator of your car, you
feel as if you are being pushed back into the seat, but there is no force pushing you
backward. You feel pushed backward due to inertia because you are in your original state
of motion and the car is accelerating.
Circular motion is similar to linear motion except that the object is rotating rather than
moving in a straight line. The concepts and variables of linear (translational) motion have
analogs in rotational motion. The important concept in circular motion is that while
you are traveling in a circular path at a constant speed you are accelerating. This
acceleration is called centripetal acceleration and points toward the center. The force
keeping an object in a circular path is called centripetal force or the center seeking force.
Some of the questions that will be answered in this unit are: Why do quarterbacks spiral
the ball when they throw a pass? Why are the starting positions on a racetrack staggered?
Why do tall chimneys break near the middle as they topple? How do you stay in
amusement park rides that go upside down? Why are curved roadways/racetracks
banked? Why are there so many pieces of truck tire tread lying on the interstate
highways? How are ice skaters able to spin so fast? Why are divers, cheerleaders, and/or
gymnasts able to do more rotations in the tuck position than the layout position? Why is it
difficult to open a door when you push on the side near the hinges?
Lesson 1: Circular Motion
In this lesson, our study will begin with the development of kinematic and dynamic ideas
can be used to describe and explain the motion of objects in circles. Newton 's laws of
motion and kinematics principles are applied to describe and explain the motion of
objects moving in circles; specific applications are made to roller coasters and athletics.
Check it Out!
Hand tossed or regular crust? Ride more merry-go-rounds! DVDs! Does it rotate or
revolve? A football spirals when released by the quarterback – why? A popular
demonstration of many physics teachers is to swing a bucket of water around in a vertical
circle fast enough so that the water doesn’t spill out when the pail is upside down. How
is this possible? Circular motion is everywhere in our real lives from pizza spinning and
rotating restaurants to skaters and divers to amusement park rides and NASCAR racing to
throwing a shot put at a track meet. How are these events related to each other?
6.1.1 Understanding and Applying Circular Motion
Web Walk
It is important to go to the sites in order and follow the directions as given.
If there is a related assignment, it will be clearly indicated. You may want
to take notes as you move along the Web Walk.
Go to
http://www.batesville.k12.in.us/physics/PhyNet/Mechanics/Circular%20M
otion/circular_motion_notes.
View the powerpoint and take notes.
Go to
http://www.glenbrook.k12.il.us/gbssci/phys/Class/circles/u6l1e.html (The
Physics Classroom) “Applications of Circular Motion” for the connection
of circular motion to the Laws of Motion. Note the suggested method for
solving circular motion problems. You will be expected to solve circular
motion problems and the method prescribed above will serve you well as
you approach circular motion problems. “Check Your Understanding” is
good practice in solving circular motion problems.
Click “next” to go to Amusement Park Physics applications. Pay careful
attention to the animations and sample problems. “Check Your
Understanding” is good practice in solving circular motion problems.
Click “next” to go Athletics and the applications of circular motion. Note
how the sample problems are done and do the “Check You
Understanding.”
Respond to the following questions and submit your
repsonses to your Notebook.
1. Many pizza places offer “hand tossed” pizza. Traditionally pizza
makers form the crust by throwing the dough up in the air and
spinning it. Why does this make the pizza crust larger?
2. An amusement park ride spins riders around on swings attached by
cables from above. What causes the swings to move away from the
center of the ride when the center column begins to turn?
3. Why would you weigh slightly less at the earth's equator than you
would at the poles?
4. A girl at the state fair is spinning a ball attached to a string in a
vertical circle. Is the force applied by the string greater than or
equal to the weight of the ball at the bottom of the ball's path?
6.1.2 Lab Activity - Going In Circles
Purpose: How does radius, mass and period influence centripetal force?
Safety Note: Safety concerns are minimal; however, common sense should
prevail while doing this activity. Eye protection is recommended.
Materials : Ball point pen tube, 2 m of string, paper/plastic cup, paper clip,
30 metal washers, stop watch, tape, meter stick, candy (wrapped is better –
in case you spill, you can still eat it without invoking the 5 second rule!)
Submit your completed report to your lab notebook. Include
the data collected, the graphs, and the interpretations/analysis.
6.1.3 Online Problem Solving
Go to
hyperphysics.phy-astr.gsu.edu/hbase/circ.html
Circular Motion – Centripetal Acceleration
Click “Calculation” and do some calculations
for practice.
Show at least 1 in your notebook.
Click “Discussion of concept” for a review of centripetal force and
centripetal acceleration. While you are on this page,
click the “centripetal acceleration” link and practice a few centripetal
acceleration calculations. When you have tried a few problems,
click “go back” (lower right corner).
Click
Centripetal force on banked highway curve
Study the problem and practice a few sample centripetal force
calculations. do some calculations for practice. Show
at
least 1 in your notebook.
Go to
id.mind.net/~zona/mstm/physics/mechanics/curvedMotion/circularMotion
/problems/cm0.htm
(Zona Land Physics) Circular Motion Problems and solve problems 11,
14, 16, 17, 18, and 20. Note: You can use the help button as a self check.
Show your work for problems 14,16, 18 and 20 in
your notebook.
Go to
dept.physics.upenn.edu/courses/gladney/mathphys/hmwrk_week_4.html#
prob_4_5
and solve problem 4.5 (PSYW). Submit your solution, with
the work shown, to your notebook.
6.1.4 Quiz - Circular Motion
To summarize, an object in uniform circular motion experiences an inward net force.
This inward force is sometimes referred to as a centripetal force, where "centripetal"
describes its direction. Without this centripetal force, an object could never alter its
direction. The fact that the centripetal force is directed perpendicular to the tangential
velocity means that the force can alter the direction of the object's velocity vector without
altering its magnitude.
Lesson 2: Center of Gravity
In this lesson the following questions will be considered: Why doesn't the Leaning Tower
of Pisa fall over? Why does the Hummer have such incredible maneuverability? How do
tightrope walkers keep their balance? Why do they carry such long poles? How does
learning physics help high jumpers set records?
6.2.1 Center of Gravity Lab Activity
How were the massive trilithon stones of Stonehenge ever put into
place? A Nova team investigated one possible method--shifting the
stone's center of gravity to make it stand upright. Read the article, then
find out how to recreate the Nova experiment using a cardboard
model.
Secrets of Lost Empires I—Stonehenge
Ancient structures may generate awe and provide
information about the people who built them, but they
leave many questions unanswered: How were they
constructed? What technologies were available to the
builders? What tools did they use?
Stonehenge
Stonehenge distinctive feature of this stone site are
the trilithons, which consist of two upright stones
topped by a horizontal lintel stone. In this program,
the NOVA team considers how to transport and raise the
massive stones, as well as how to place the lintel
stone on top. By comparing different strategies and
adapting ramps, levers, and other tools that might have
been available to the ancient builders, the team works
to meet the challenge.
http://www.pbs.org/wgbh/nova/teachers/activities/2403_sle1ston.html
For Activity 6.2.1 "The Great Trilithion Balancing Act", you will need the following:
student handout (print from the web site), string, 15 cm (6 in.) long, washer, cardboard
(about .1 mm, or 1/32 in., thick), scissors, several large paper clips, pencil with flat
eraser, hole puncher, and a ruler.
Submit Answers to your Notebook
6.2.2 Center of Gravity Practice Quiz
Go to
www.batesville.k12.in.us/physics/PhyNet/Mechanics/CenterOfMass/Cen_Mass_Quiz.ht
ml
click on the practice quiz and answer the questions for a review of Center of gravity.
Submit your score to your Notebook
6.2.3 Center of Gravity Demonstrations and Review
Join me for demonstrations and discussion of center of gravity, center
of mass, and toppling.
During the demonstrations and discussion consider the following
questions to ponder:
Why is the middle or aisle seat in a bus or airplane the most comfortable
when the road or air is bumpy?
How is a baseball bat standing on its handle or on its head be likened to
the different centers of gravity in women and men?
If you are sitting in a chair, why is it not possible to stand up without
putting your feet under the chair?
Why can't you touch your toes if you are standing with your heels against
the wall? You are standing on the edge of a cliff and a friend nudges you
from behind. Describe the reaction of your body in terms of motion and
center of gravity.
At the conclusion of the Center of Gravity
demonstrations, complete the Question/s to ponder
and submit your answers to your notebook.
6.2.4 Quiz – Center of Gravity
Check it Out!
At this point you should have an understanding of and be able to apply the concepts of
toppling, stability, center of gravity, and center of mass to many everyday events. The
center of gravity and the center of mass are important concepts in the study of circular
motion. They not only are applicable to everyday situations, but also are a key to
understanding rotational mechanics, the next lesson in this unit.
Lesson 3: Rotational Mechanics
Everyone enjoys watching an ice skater finishing a performance with a spin. The
impressive skill demonstrated along with some interesting physics makes for quite a
sight! Skaters may not understand the physics involved, but they are very good at
applying it! Rotational dynamics (and kinematics!) concepts and variables are very
similar to translational (linear) dynamics (and kinematics!). In this lesson we will
consider the dynamic variables that are analogs to linear dynamics quantities. Some
questions to ponder during this lesson are: Why do quarterbacks spiral the ball when they
throw it? Why are there so many pieces of truck tire tread lying on the interstate
highways? How are ice skaters able to spin so fast? Why are divers, cheerleaders, and/or
gymnasts able to do more rotations in the tuck position than the layout position?
6.3.1 Virtual Lab – Torque
Purpose: What is the relationship between forces and distances from the
fulcrum for a balanced see-saw?
Discussion: An object at rest is in equilibrium and the sum of the forces
acting on it is zero. Because the object has no rotation, the sum of the
torques is zero. When a force causes an object to start turning or rotating, a
nonzero net torque is present. Suppose that you are an animal trainer and
you want to balance a 600 kg gorilla on a see-saw using only your own
body weight. If your mass is 50 kg and the gorilla is 2.0 m from the
fulcrum, how far from the fulcrum must you sit on the other side to
balance the gorilla?
OBTAIN LAB FROM INSTRUCTOR
6.3.2 Rotational Derby Lab
Purpose: How does the rotational inertia affect the rate of
rotation?
OBTAIN LAB FROM INSTRUCTOR
6.3.3 Online Concept/Problem Review
Go to
btc.montana.edu/olympics/physbio/biomechanics/cam02.html
( University of Montana ) Conservation of Angular Momentum. Review
the animations. Go to
www.nasaexplores.com/show_912_student_st.php?id=04021991438
(NASA Explores) Angular Momentum. Solve the problems. Click “Go to
teacher sheet” and scroll down to check your answers.
Go to
www.batesville.k12.in.us/physics/PhyNet/Mechanics/RotMechanics/Rot_
Mech_Quiz.html
Practice Quiz. Do the practice quiz and submit your
score to your notebook.
6.3.4 Lesson Wrap Up – Physics Thoughts for
Discussion
Answer the questions and Respond to at least 2
other persons with a thoughtful comment to your
notebook
1. Which will roll with a greater acceleration down an incline, a can
filled with water or a can full of frozen water?
2. A basketball player wishes to balance a ball on his/her finger tip.
Will he/she be more successful with a spinning ball or a stationary
ball? What physics supports your answer?
3. Why is it incorrect to say that when a cheerleader executes a
somersault and pulls her arms and legs inward, her angular
momentum increased?
Knowledge Check
Figure Skater Spins
Everyone has seen the classic spin in figure skating, where the skater draws her arms and
a leg in and speeds up tremendously. This is the result of conservation of angular
momentum : as the skater reduces her rotational inertia by pulling her arms and leg in, her
rotation speed must increase to maintain constant angular momentum. Angular
momentum conservation plays an important role in all figure skating routines. Watch the
video clips of skaters spinning. Why do they spin faster when they pull their arms
inward?
www.bsharp.org/physics/stuff/skater.html
The Physics of Everyday Stuff
Lesson 4: Unit Wrap Up
Unit Assessment