# Force & Motion

## Demonstrating Rotational Inertia

Have you ever struggled to describe Rotational Inertia to your students? Even worse, have you ever struggled to understand Rotational Inertia yourself? Did you know Rotational Inertia is the same as Moment of Inertia? Yeah, I’m with you there. I did not know the name had been changed until recently. However, I do think Rotational Inertia is a more logical phrase than Moment of Inertia. Well, if you would like some help with the concept of Rotational Inertia, then I highly suggest the Rotational Inertia Demonstrator from Arbor Scientific because it is an easy way to demonstrate the concept of rotational inertia. The demonstrator is composed of three pulleys of different sizes all centered around the same axle. Attached to the pulleys are four spokes on which four masses can be placed. The distance from the axle, or axis of rotation, of the four masses on the spokes can be adjusted.
In order to understand rotational inertia, we should first review the equation for rotational inertia of a system of particles:
The rotational inertia of a system of particles equals the sum of the quantity of the mass of each particle times the square of the distance each particle is from the axis of rotation. While the Rotational Inertia Demonstrator does not appear to be a system of particles, the equation for the rotational inertia of a system of particles helps us to understand how the rotational inertia of the demonstrator changes when we adjust the locations of the four adjustable masses. The closer the four adjustable masses are to the axle, or axis of rotation, the smaller the “r” value in the rotational inertia equation and the smaller the rotational inertia of the demonstrator.
We also need to review the Rotational Form of Newton’s Second Law of Motion to better understand rotational inertia. The net torque acting on an object equals the rotational inertia of the object times the angular acceleration of the object. Please remember torque and angular acceleration are vectors.
Notice the similarities to the Translational Form of Newton’s Second Law of Motion. The net force acting on an object equals the inertial mass of the object times the linear acceleration of the object. Again, remember force and linear acceleration are vectors.
Force is the ability to cause a linear acceleration of an object.

Torque is the ability of a force to cause an angular acceleration of an object.

Torque is the rotational equivalent of force.

Rotational inertia is the rotational equivalent of inertial mass.

Angular acceleration is the rotational equivalent of linear acceleration.

But, what does it mean that rotational inertia is the rotational equivalent of inertial mass? Inertial mass is the measurement of the resistance of an object to linear acceleration. Therefore, rotational inertia is the measurement of the resistance of an object to angular acceleration. In other words, the greater the rotational inertia of an object, the more that object will resist an angular acceleration. Referring to the rotational inertia demonstrator, the farther the four adjustable masses are from the axis of rotation, the larger the “r” value in the equation for the rotational inertia of a system of particles, therefore the larger the rotational inertia of the demonstrator. The larger the rotational inertia of the demonstrator, the larger the resistance of the demonstrator to angular acceleration. In summary, the larger the distance the four adjustable masses are from the axle, the larger the rotational inertia, and therefore the larger the resistance of the demonstrator to angular acceleration.
This is demonstrated below by hanging a 100 g mass from the largest pulley in two simultaneous demonstrations. In the demonstration on the left, the four adjustable masses are close to the axis of rotation and therefore the rotational inertia of the system is smaller. In the demonstration on the right, the four adjustable masses are farther from the axis of rotation and therefore the rotational inertia of the system is larger. When both demonstrators are simultaneously released from rest, because the net torque caused by the 100 g masses is approximately the same, the demonstrator with the larger rotational inertia on the right has a smaller angular acceleration. In other words, the demonstrator with the larger rotational inertia speeds up rotationally at a slower rate. Going back to the Rotational Form of Newton’s Second Law of Motion, because the net torque is almost the same, a larger rotational inertia results in a smaller angular acceleration:
Notice we are always keeping the four adjustable masses the same distance from the axle, or axis of rotation. This is to keep the center of mass of the system at the axis of rotation of the system. When the four masses are not equally spaced from the axis of rotation, then the center of mass of the system is offset from the axis of rotation and the force of gravity acting on the system causes a torque on the system. The force of gravity causing a torque on the system makes understanding the demonstration much more complicated. In the examples shown below, the demonstrator on the left with four masses equally spaced from the axle rotates at almost a constant angular velocity. The demonstrator on the right has one mass farther from the axis of rotation and therefore the whole system actually becomes a physical pendulum. The system oscillates back and forth in simple harmonic motion. While this is interesting, it does not provide an obvious way to learn about rotational inertia. In summary, it is much easier to learn about rotational inertia from the demonstrator if all four masses are equally spaced from the axis of rotation.
Let’s look at another set of demonstrations below to learn about rotational inertia. As in the previous demonstration, on the right, we have a 100 g mass hanging from the largest pulley and all four adjustable masses far from the axis of rotation. On the left, all four adjustable masses are still far from the axis of rotation, however, the 100 g mass is hanging from the smallest pulley instead. In other words, both rotational inertia demonstrators have the same rotational inertia and the force of gravity acting on the string is the same, however, the net torque acting on each demonstrator is different. Recall torque equals the “r” vector times the force causing the torque times the angle between the direction of the “r” vector and the direction of the force. The magnitude of the “r” vector is the distance from the axis of rotation to where the force is applied to the object:
Because the 100 g mass is hanging from the small pulley on the left and the large pulley on the right, the “r” vector for the small pulley is smaller and therefore the net torque acting on the demonstrator through the small pulley is less. Therefore, according to the Rotational Form of Newton’s Second Law of Motion, the angular acceleration of the demonstrator on the left is less than the angular acceleration of the demonstrator on the right.
Our last set of demonstrations has both demonstrators with identical rotational inertias and masses hanging from the smallest pulleys. Also, both demonstrators have a 100 g mass hanging over the left side of the pulley. However, the demonstrator on the right has a second mass, a 200 g mass, hanging over the right side of the pulley. This means the demonstrator on the right has two different masses hanging off of the smallest pulley.
In order to determine what is going to happen, remember the Rotational Form of Newton’s Second Law of Motion includes net torque, not just torque.
In this example, the net torque from the two masses on the demonstrator on the right actually has roughly the same magnitude as the net torque acting on the demonstrator on the left, however, the directions are opposite from one another.
Again, both demonstrators have the same rotational inertia, are using the same pulley, and have a 100 g mass hanging over the left side of the pulley. The pulley on the right adds a 200 g mass hanging over the right side of the pulley. For the demonstrator on the right, the 100 g mass hanging over the left side of the pulley essentially cancels out 100 g of the 200 g mass hanging over the right side of the pulley. This effectively means the right demonstrator essentially has a 100 g mass hanging over the right side of the pulley. Therefore, the net torques on both demonstrators have essentially the same magnitude and opposite directions. Therefore, the angular accelerations of both demonstrators should have roughly the same magnitude and opposite directions. You can see that is true in the demonstration.
But why do the two demonstrators have “roughly” the same magnitude angular accelerations? Adding the 200 g mass to the demonstrator on the right increases the total mass of the system. Because inertial mass is resistance to acceleration, increasing the total mass of the system actually decreases the angular acceleration of the system a little bit, even though the net torque should be roughly the same. Proving this requires drawing free body diagrams, summing the torques on the wheel, and summing the forces on each mass hanging, so I am not going to walk all the way thought that solution here.
There are many more ways you can make adjustments to the rotational inertia demonstrator to better help understand rotational inertia. For example, ask yourself what would happen to the angular acceleration of the demonstrator if the only change we make to it is to increase the mass hanging from the demonstrator? Increasing the mass hanging from the demonstrator increases the net torque acting on the demonstrator. The rotational inertia remains the same. Therefore, according to the Rotational Form of Newton’s Second Law of Motion,  , the angular acceleration of the demonstrator will increase.
What if the only change we make is to change the locations of the four adjustable masses from all being at their farthest extreme positions to having two of the adjustable masses near the axis of rotation and two adjustable masses far from the axis of rotation? Bringing two adjustable masses near the axis of rotation decreases the rotational inertia of the system and therefore, according to the Rotational Form of Newton’s Second Law of Motion, the angular acceleration of the demonstrator will increase. Notice, this will only work when the two close adjustable masses are opposite one another and the two far adjustable masses are also opposite one another. If this is not the case, the center of mass of the rotational inertia demonstrator will not be at the axle, or axis of rotation, which is a problem we addressed earlier.
The pulley sizes of the rotational inertia demonstrator are provided by Arbor Scientific. They are 20.22 mm for the small pulley, 28.65 mm for the medium pulley, and 38.52 mm for the large pulley. Given this information, we can even predict which way the rotational inertia demonstrator will rotate if we were to hang 100 g over one side of the large pulley and 200 g over the other side of the small pulley. Before releasing the demonstrator, the angular acceleration of the demonstrator is zero because it is at rest. Therefore the torque caused by the 100 g mass will be 0.3852 meters times 0.100 kilograms times 9.81 m/s2 times the sine of 90 degrees which equals roughly 0.38 N.
The torque caused by the 200-gram mass will be 0.2022 meters times 0.200 kilograms times 9.81 m/s2 times the sine of 90 degrees which equals roughly 0.40 N.
Therefore, the net torque caused by both masses acting on the demonstrator before it starts to accelerate is the difference between these two torques because they act in opposite directions.
Therefore, because the torque caused by the 200 g mass is larger than the torque caused by the 100 g mass, the rotational inertia demonstrator will rotate in the direction caused by the torque of the 200 g mass.
Please realize these torque calculations are only correct while the demonstrator is at rest. Once the demonstrator begins to accelerate, the force of gravity and the force of tension acting on the mass hanging are no longer the same and we would need to draw free body diagrams and sum the forces on each hanging mass.
If you enjoyed watching this video by Jonothan Palmer, the creator of Flipping Physics, please let us know in the comment section below and check out his YouTube page for more videos like this one.

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The Lab4Physics App is a helpful tool for teaching physics and physical science. It is a lab app for smartphones and tablets, and because of the familiar controls and friendly, easy-to-use interface, all your students can use it

 The App works by using the built-in features of cell phones and tablets that convert easily to probeware, such as the accelerometer, which we will explore first. Fig 1.  The Lab4Physics home screen.  When you open the app, there are lots of experiments you can try (which are categorized on the left) or you can go straight to the tools (right) and perform your own experiments.

ACCELEROMETER

 If you shake the phone up and down, the accelerometer records this motion in 3D. Deleting the X and Z axis, we will now graph only the Y-vertical motion. Fig 2.  It is easy to use the accelerometer to measure the earth’s gravity field strength.  Here the phone was held vertical then slowly turned to lay flat.  The gravity constant 9.8 m/s2 is measured. The app allows you to zoom in, both vertically and horizontally, and slide the image around, just like a picture or map.  Because this interface is so familiar, students will already know how to do this. Fig 3.  The phone’s Acceleration is measured in 3 dimensions, but typically you only need one. Because the accelerometer is so easy to use, you will find yourself using it in many different applications, such as spring and pendulum experiments.  Note that when facing the phone, X is right and left, Y is up and down, and Z is toward and away.  The positive axes are right, up, and toward, which you can remember with thumb X, open fingers Y, palm-slap Z. Fig 4.  Zoomed-in on the image of the above data.  Vertical zoom for precise amplitude measurements and horizontal zoom for precise time (period) measurements. Fig 5.  A plastic bag is a convenient container for the phone when performing spring and pendulum experiments.  The touchscreen still works fine through the plastic.

SONOMETER

 Using the microphone, Lab4Physics can analyze the intensity and frequency of a sound that the phone records. With this device, you can see the waveform of the frequencies that the phone picked up. Use this to compare the amplitudes of loud and quiet sounds or the frequencies of a high and low pitch.  This works as an instant oscilloscope. It is also possible to measure the period as the time between peaks, it helps to zoom in for this. Fig 6.  The Sonometer makes a measurement of the author’s whistling ability.  The period can be measured as the peak to peak time, or the Highest peak frequency can be displayed automatically by using the Intensity vs. Frequency feature. The waveform displayed looks transverse, but the sound is a longitudinal wave.  Therefore, it is important to explain how this wave was generated.  It was the motion of the vibrating microphone that moved a small magnet that generated the electricity that became the signal displayed. The device also can calculate the frequency of the loudest part of the signal it is detecting.  This can be used to test who sings with the highest or lowest frequency or just to check the frequencies of musical instruments. Fig 7.  A tuning fork, which is supposed to be the musical tuning standard A 440Hz, is revealed to be very nearly correct by the Lab4Physics App’s Sonometer feature.

CAMERA / MOTION TRACKING

 One of the most useful features is the ability to track an object’s motion.  Utilizing the phone’s camera, film an object (usually with a ruler in the picture), and by tracking at a specific point on the object, you can follow its motion through the frames of footage. Fig 8.  An accelerating toy car has its motion tracked through ten frames of footage generating the expected parabola of an accelerating object. Because the frames are equally separated by time intervals the app can turn this data into a distance vs. time graph.  From this data, it further generates the acceleration and velocity graphs.  Even a Data Table is provided so you can sort out anomalous data or analyze further.

SPEEDOMETER

 Lab4Physics also has a speedometer which is a streamlined alternative to stopwatches.  Students can, for example, set up a series of positions and click the split button to get the individual times for when the object is at that position.  Using this, graphs are generated for position and velocity. Fig 9. A typical Speedometer experiment. Tracking the position of a toy car through space. Changing it from going slow to fast can show up on a position vs. time graph.

EXPERIMENTS AND LABS

 Lab4Physics has lots of ready to go labs to instruct your students, or you can use them to give you ideas.  Here we explore some of the labs on waves. Fig 10.  Left, a screenshot from the app shows the four labs on waves.  Choosing Do-Re-Mi takes us eventually to this screen, right, which shows how we will be exploring the frequency of a musical instrument. The labs take the students through the experiment in five or six steps.  They are self-contained and complete and let you know how much time the activity should take.

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## Air Powered Projectile in-depth look [W/Video]

The Air Powered Projectile in-depth look

One of the best ways to engage your students in the study of projectile motion is with direct experiment and observation. For this purpose I recommend the air-powered projectile. It safely and reliably demonstrates projectile motion by simply releasing compressed air. Here are five experiments to get you started.

The soft nose cone provides a high degree of safety while the body’s sleek design minimizes the effects of air resistance.

MEASURE LAUNCH VELOCITY
Shooting the projectile straight up is the easiest way to determine launch speed.
The first thing you want to do is determine the launch velocity by shooting straight up. It takes about 5 seconds to go up and come back down when shot vertically. Use the formula v=vo+at , analyze the top of the trajectory. At this point velocity = zero. Then set gravity to negative 10m/s/s. Gravity is pulling opposite the initial launch velocity, which is the unknown. Plugging in 2.5 seconds for time (assuming the trip takes the same time up as down) we get a launch velocity of about 25m/s. You might be concerned whether this is a safe speed, but the soft nose c one, and the fact that there is no chemical propellant ensures this. You may wish to wear safety goggles anyways.

The calculation of launch velocity is straight forward, requiring only algebra.

ANGLE vs RANGE
A classic experiment that I have done every year since I started teaching is to investigate which angle generates the greatest launch distance. Students will have their own hypothesis. Without doing any math, try to hypothesize which angle will maximize the range. This is an experiment that works in both high school and middle school. The theoretical result is that 45 degrees maximizes range.

Sample data for the Range vs Angle Experiment. Note the systematic error on the zero.
This is because the product of horizontal velocity and time in the air is maximized. The mathematical proof is a common homework problem in Honors Trigonometry classes and can be done without calculus. When you plot the data, a surprising result is that the complementary angles, like 30 and 60 degrees can have the same range as each other. This is because when the velocity is more horizontal, the vertical time is lessened, and vice versa.

Angled Wooden Wedges help a lot in this experiment. The angle of launch will be the compliment to these angles.
When performing this experiment, it is helpful to use the angled wooden wedges option. These help adjust the angle without the use of clumsy blocks of wood or coupling. Another addition you might want to invest in are the varied speed end caps. The different size caps affect the pressure limit that causes the seal to slip, launching the tube upward with the force of expanding gas. Larger endcaps can capture more of that force so it will go faster. This adds another variable which allows you to make new predictions. But with the same endcap, you get the same time, every time.

Different sized end caps can change the launch velocity, adding a new variable.
The air powered projectile does not use any chemicals to launch. It only uses the compressed air of a bike pump, typically around 60 psi (pounds/square inch). When you launch the projectile, you will usually see some clouds appearing beside the base. They only last for a second, but can be made more visible by using a high speed camera. (Many students now have these in their smartphones.)

Adiabatic clouds appearing during a typical launch event. This image was taken with an iPhone 5s in 120 frames/second mode.
The clouds are caused by the humidity in the air being turned into a vapor due to the rapid temperature change. When a gas expands rapidly, it cools. This is called adiabatic expansion. It is an important idea in thermodynamics and this is a really good example of it. You’ve probably seen it when you open a champagne bottle, or even a soda.

Because the force of launch only acts in the initial moment, the rocket is an excellent example of a free falling projectile (unlike missiles and rockets). The sleek profile minimizes air resistance and turbulence while increasing the accuracy of the experiment.

HIGHLY ACCURATE CALCULATED LANDING SITES
In video we launch the air powered projectile at 30 degrees, and from the first experiment, we already know the initial velocity, Vo=25m/s. We use Vo sin30 to find the initial upward velocity (12.5m/s) and Vo cos30 to find the horizontal component (21.6 m/s).

A typical projectile motion problem can now be performed experimentally, with a high degree of accuracy and while being highly engaging.
At the highest moment, it is only moving horizontally, so we once again can use v=vo+at. Only this time the plug step is 0=12.5-10t giving a time of 1.25 seconds to reach the top. Twice that is 2.5 seconds, the total time of flight.
The product of the horizontal component and the total time of flight is the distance traveled. (The horizontal velocity never changes.) The range, x=vhoriz * time = 21.6m/s * 2.5 sec = 54 m.
That the theoretical prediction. Take it with you, and some measuring tape (or the yard lines on the football field) and see what really happens.

The impact location proves to be within 2 meters of the expected value.
When we did the experiment we got a result of 56 meters. That is less than 4% error, very good!

James Lincoln

Tarbut V’ Torah High School

Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and  the UCLA Physics Video Project.

Contact: [email protected]

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## Measuring Forces on an Inclined Plane

The Forces on an Inclined Plane Demonstrator is a new piece of physics equipment that can help make the abstract concepts of vector components of forces a tangible reality.  The innovation of the device is that it can be manipulated at will.  The angles can be set and reset quickly and the forces measured fairly quickly.

The device breaks the weight of an object into its component forces and allows for accurate data to be taken without having to set up clumsy and cumbersome ramps.

Each module comes with a built in scale (that measures how the Normal Force varies with the angle of inclination) and a parallel spring scale (that measures how the Parallel Force increases with the angle of inclination).

The module contains three unique features.  Built in scale, protractor, and spring scale  mount.

The measurements rely heavily on Balanced Forces.  Balanced Forces result in zero acceleration.  The action of gravity pulling the cart downhill is balanced by the equal and opposite action of the spring scale pulling the cart uphill.  Similarly, the component of the weight that is wasted in the hill is balanced by a reaction force which is perpendicular to the hill.  This is called the Normal Force (normal meaning perpendicular).

The sine and cosine relationships will come naturally out of well-calibrated data.

Lab Ideas

Create Graphs of Sine & Cosine:  The two forces measured by the device will trace out the sine and cosine curves (with an amplitude mg) as the device is rotated through angle.

Verify Specific Predictions:  Test out the special triangles: 45 45 90, 30 60 90, 3 4 5, to reinforce the behavior of the forces as the vary with tilt angle.  For example, 5N tilted to an angle of 37 degrees will have a normal force of 4N and a downhill force of 3N.  But what will happen for 53 degrees?

In an open-ended lab the students invent their own procedures and hypothesize the relationships without formal instruction.

Open-Ended Lab:  Have students try to invent the formulas for themselves.  Taking data from the digital balance and from the spring scale to determine the relationships from scratch.  This style of lab is consistent with the NGSS Standards and the AP Physics 1 curriculum.

Tips for Success

While taking measurements the user will have to “tare” the scale every time.  This is because the plate that sits on the scale is itself an object with weight.  Once the angle is selected, simply lift the cart and tare then reweigh.

It is also important to recalibrate the spring scale when making a measurement of the component downhill.

How it looks to correctly set 45 degrees.

Be careful not to confuse the screw that holds the up the incline plane with the angle indicator.  The angle is measured best by the lower edge of the plane being in line with the angle in question.

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James Lincoln

James Lincoln is an experienced physics teacher with graduate degrees in education and applied physics. He has become known nationally as a physics education expert specializing in original demonstrations, the history of physics, and innovative hands-on instruction.

The American Association of Physics Teachers and the Brown Foundation have funded his prior physics film series and SCAAPT’s New Physics Teacher Workshops.

Lincoln currently serves as the Chair of AAPT’s Committee on Apparatus and has served as President of the Southern California Chapter of the AAPT, as a member of the California State Advisory for the Next Generation Science Standards, and as an AP Physics Exam Reader.  He has also produced Videos Series for UCLA’s Physics Demos Project, Arbor Scientific, eHow.com, About.com, and edX.org.

## See Energy Transformation with a thermal camera or steel spheres [W/Video]

You can calculate the thermal energy created when the ball hit the bat by using the Law of Conservation of Energy. Before the collision, the center-of-mass of the bat (mass 1kg) was moving at about 70mph (31m/s) and the ball (mass 0.15kg) was moving at about 90mph (40m/s). Now, calculate the initial kinetic energy.

After the collision, let’s estimate the speed of the bat at 50mph (22m/s) and the speed of the ball is 30mph (13m/s). Calculate the final kinetic energy. [Answer: 255J]. Now use the Law of Conservation of Energy to find the thermal energy created during this ball-bat collision. [Answer: 345J]

This thermal energy is detected by the camera as a higher temperature on the bat and ball. The camera shows higher temperatures as white.

Now you can try to estimate the thermal energy created the collision of the Colliding Steel Balls? What information do you need to find or estimate? Paper burns at about 200˚C. Do your numbers suggest that the paper’s temperature could rise that much?

Dr. David Kagan has been at CSU Chico for over thirty years. During this time, Dr. Kagan has served in numerous roles including: Chair of the Department of Physics; founding Chair of the Department of Science Education; and Assistant Dean in the College of Natural Sciences to name a few. He is a regular contributor to The Physics Teacher having had over thirty papers published in the journal. Kagan continues his deep devotion to quality teaching by avidly engaging his students with methodologies adapted from the findings of Physics Education Research. In addition, he has remained true to his lifelong obsession with baseball by using the national pastime to enhance the teaching and learning of physics.

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# Back to School Means Back to STEM

The Next Generation Science Standards (http://www.nextgenscience.org/next-generation-science-standards) identifies eight practices of science and engineering as essential for all students to learn. These are:

1. Asking questions (for science) and defining problems (for engineering)
2. Developing and using models
3. Planning and carrying out investigations
4. Analyzing and interpreting data
5. Using mathematics and computational thinking
6. Constructing explanations (for science) and designing solutions (for engineering)
7. Engaging in argument from evidence
8. Obtaining, evaluating, and communicating information

One of the best ways to implement all of these practices is through the growing practice of Project Based Learning (PBL), defined by Edutopia as “a dynamic classroom approach in which students actively explore real-world problems and challenges and acquire a deeper knowledge” (http://www.edutopia.org/project-based-learning). The duration of these projects can be as short as a single class period or last throughout an entire school year, but typically last from 1-3 weeks.

This past summer, Grade 6 – 9 science teachers, math teachers, and administrators from Warsaw (IN) Community Schools partnered with science and math educators from Ball State University during a two week summer institute to design classroom projects, strengthen science and math content knowledge, and refine inquiry practices. The Arbor Scientific “Pull-Back Car” (http://www.arborsci.com/pull-back-car) was featured in a “mini” PBL activity to illustrate how science, technology, engineering, and mathematics (STEM) can be integrated into an authentic data collection and analysis activity.

Participants were divided into 12 groups and each group of 4-5 participants was given a pull-back car. Each participant played the role of a quality control engineer, whose job description may include taking “part in the design and evaluation of the product” and being “responsible for making sure that the materials meet the requisite standards and that the equipment works correctly” (http://www.wisegeek.com/what-is-a-quality-control-engineer.htm). Each group served as a team of quality control engineers who were instructed to design and conduct tests on these cars to determine if Arbor Scientific should continue selling them.

1. 1. How consistent is the distance an individual pull-back car travels after being pulled back a specified distance?
2. 2. How consistent is the amount of time an individual pull-back car travels after being pulled back a specified distance?
3. 3. How straight does an individual pull-back car travel?
4. 4. Do all pull-back cars behave similarly?

Each team was charged with designing an experiment to answer their quality question, conducting the trials, analyzing their results, summarizing their findings on poster paper, and reporting their results to the large group.   Groups scattered in and around the building to design and conduct their trials.

After completing the data collection portion of the activity, groups returned to their tables to analyze their data and report their results.

After each group had completed their tasks, each group presented their findings. Examples of summary posters are shown below.

Once the participants had a good idea of how consistent the cars were, these cars were again used later in the summer institute to investigate additional inquiry questions, such as:

1. 1. How does the distance the car is pulled back before release affect the total distance it travels?
2. 2. How does the distance the car is pulled back before release affect the total time it travels?
3. 3. How does additional weight affect the distance the car travels when pulled back a specified distance?
4. 4. How does additional weight affect the total time the car travels when pulled back a specified distance?
5. 5. How does the angle of incline affect the distance the car travels when pulled back a specified distance?
6. 6. How does the angle of incline affect the total time the car travels when pulled back a specified distance?

Despite slight inconsistencies in the behaviors of the cars, participants in this summer institute agreed that the Arbor Scientific Pull-Back Car is an excellent inexpensive product that can be used in many different investigations – especially when one wants to integrate aspects of STEM. These cars can be used at any grade level and provide countless opportunities for students to engage in authentic scientific inquiry. They also provide an inexpensive way for math teachers to incorporate real world data collection and analysis. As a science educator, I heartily recommend this product and can honestly say that I consider it the ultimate inquiry device!

Dr. Joel Bryan

Ball State University

Muncie, Indiana

Dr. Bryan teaches at Ball State for the Department of Physics and Astronomy. He taught all levels of high school physics (Pre-AP, AP, conceptual) and a variety of mathematics courses for 13 years before receiving his Ph.D. in curriculum and instruction at Texas A&M University.

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## Measuring the Acceleration with the g Ball

Galileo claimed that all objects fall toward Earth with the same acceleration. Modern measurements indicate that this acceleration is about 9.8m/s2. Using the G-Ball by Arbor Scientific, you can measure this value and compare the acceleration of other objects with different masses and in different states of motion.

What do I need?
You need a G-Ball, a meter stick, other objects to drop such as a baseball.

What will I be doing?
First, you will measure the acceleration due to gravity by simply dropping the G-ball and getting the time to fall.  Next, you’ll throw the G-ball horizontally at different speed and see if the time of fall changes.  Finally, you will drop the G-ball and a baseball to see which object accelerates more rapidly.

What do I think will happen?
Assume that you drop the G-ball from rest from an initial height of 1.0m.  Use the accepted value of g = 9.8m/s2 and the kinematic equation  to predict the time of fall.  Did you get 0.45s?

If you toss the G-ball horizontally, at different speeds do you think:

1. The time for the fall will increase if the G-ball is thrown faster.
2. The time for the fall will stay the same if the G-ball is thrown faster.
3. The time for the fall will decrease if the G-ball is thrown faster.

If you drop a G-ball and a baseball at the same time which one will hit the ground first?  Again, take a moment to write down your thinking to explain your answer.

What really happened?

1. Following the instructions packaged with the G-ball, use it to time a fall of 1.0m.
2. Repeat this process several times to get an average value.
4. Time the fall for the G-ball tossed horizontally from a height of 1.0m.
5. Repeat this tossing the ball horizontally at several different speeds.
6. Do the values vary more than they did for the dropped G-ball?  Comment on your results and compare them with your prediction.
7. Drop a G-ball and a baseball from the same height at the same time.
8. Repeat this several times until you are sure which one hits the ground first.

What did I learn?
If you found that the time for the fall was about 0.45s, then you have verified the accepted value of the acceleration due to gravity is 9.8m/s2.  Did you discovered that regardless of the speed you threw the ball horizontally the time of the fall was the same?  If so, you have shown that the horizontal motion does not affect the vertical motion.  Finally, if you saw that all objects fall at the same rate, you have verified Galileo’s experiment – just like he supposed did at the Tower of Pisa.

What else should I think about?
Why did you have to be careful to throw the ball horizontally?  What would have happened if you accidentally gave the ball a slightly upward initial velocity?  What about a slightly negative initial velocity?

If the mass of a falling object doesn’t affect its motion, why does a feather fall slower that the g ball?

Catch it in the Web!
The Brainiacs dropped cars to test Galileo’s ideas about falling objects. Check it out!

A feather and a hammer were dropped at the same time on the moon. See the result!

Dr. David Kagan has been at CSU Chico for over thirty years. During this time, Dr. Kagan has served in numerous roles including: Chair of the Department of Physics; founding Chair of the Department of Science Education; and Assistant Dean in the College of Natural Sciences to name a few. He is a regular contributor to The Physics Teacher having had over thirty papers published in the journal. Kagan continues his deep devotion to quality teaching by avidly engaging his students with methodologies adapted from the findings of Physics Education Research. In addition, he has remained true to his lifelong obsession with baseball by using the national pastime to enhance the teaching and learning of physics.

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## A Visit to Isaac Newton’s Home [W/Video]

When I visited England this summer, I had the opportunity to walk in Isaac Newton’s footsteps at his birthplace, Woolsthorpe Manor.

It is a little tourist museum far from the major train stops. You will probably have to take a long taxi ride from the train station at Grantham, but it’s not so far from London that it’s more than a day trip.  Woolsthorpe means wool farm, and it still is a wool farm where you can find long-haired Lincoln Sheep grazing in the meadows.

It is everything you would imagine a farm in the idyllic English countryside to be, with lightly rolling green hills, a stone cottage, and barns. The home and birthplace of Isaac Newton still stands as it did during his lifetime: a proud stone cottage with many adjacent stables and farm houses. Today, every part that is not empty is a museum.

During the plague years, 1665-1666, Newton fled his college at Cambridge and retired home to his mother’s stone cottage beside a grove of apple trees.  He was a self-taught student of mathematics, and by the time he returned, he was the top mathematician in Europe.

It was in the apple orchard here in Woolsthorpe that Newton developed his Three Laws of Motion and Law of Universal Gravitation. The apple tree that inspired the latter is supposedly still growing here. It is gnarled with age but still gives apples.

The markers tell the story of how the tree that inspired the young Newton’s gravity theory fell victim to gravity itself during a major storm.

At well over 400 years old, this tree miraculously still bears apples and inspires those who make the pilgrimage. As the sunlight broke through the clouds and the birds sang far from the city sounds it was easy to imagine what this place was like in Newton’s time and how one could think clearly here.

The peace stretches far across the land, and there is a contemplative feeling in the air; it seems like a place where there is nothing much to do except think of ideas.

Newton was born here on Christmas Day 1642, and grew up here learning to build little mechanical toys.

Young Newton often neglected his farm duties, such as mending fences and tending to the sheep, in favor of reading and experimenting. His father passed away before he was born, and his mother remarried and left him in the care of his grandmother. These stories and others can be learned while visiting the museum that was his home.

The main building itself has five rooms, and these are decorated in the style of the era, with signs and exhibits throughout. There is even a little hands-on science museum where visitors can try out some of the classic experiments associated with Isaac Newton.

Also on site, you will find a human sundial, a place for a picnic, and the famous experiments on optics that were Newton’s other great contribution to physics. There are prisms, reflecting telescopes, and light color mixers.

When Newton came of age, he left the countryside to attend Trinity College in Cambridge. Here, you can find cloned relatives of his apple tree, grafted, through vegetative propagation. One of the trees is in the Cambridge University Botanic Garden.

Cambridge is a great day trip too, and Trinity College is beautiful, thanks to King Henry the VIII’s money. Near the front gates you will find another apple tree, right outside Newton’s office, where he lived and worked as a research professor for almost 30 years.

So where is Sir Isaac Newton now?

Some of his books and locks of his hair can be found at Cambridge and Woolsthorpe. Even a copy of his death mask resides at Woolsthorpe. The memorial and grave of Sir Isaac Newton is at Westminster Abbey in London. This is not far from where he was president of the Royal Society of London. Which also has markers that honor their famous former president.

Of all the sights, none can equal the quiet, contemplative air of the orchard in front of the stone cottage at Woolsthorpe Manor. As a physicist, this is truly a place for spiritual fulfillment.

It was during the plague years, that Newton escaped here and was inspired to write his Laws of Motion and Theory of Universal Gravitation. Spend an afternoon here and you too, may have a great idea.

James Lincoln

Tarbut V’ Torah High School

Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and  the UCLA Physics Video Project.

Contact: [email protected]

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## SpillNot: The Physics Behind the Slosh

Although the problem of why coffee spills might seem trivial, it actually brings together a variety of fundamental scientific issues. These include fluid mechanics, the stability of fluid surfaces, and interactions between fluids and structures (we’ll set aside the biology of walking for now). The SpillNot is a cool tool for getting your students interested in the everyday physics behind why drinks spill while we’re carrying them and what has to happen to prevent spillage.

Why spilling happens: When the rigid cup is accelerated horizontally the low viscosity fluid remains at rest and is left behind to rise up on the cup’s wall. The greater the acceleration is compared to gravity, the more fluid is left behind such that the ratio ahoriz/g is the same as the slope. Later, when the person stops walking forward, the cup is decelerated but the fluid (now in motion) remains in motion toward the other end of the container. In some cases there is an amplifying resonance when the accelerations match the natural frequency of the fluid’s back and forth sloshing. Try it!

Why the SpillNot doesn’t spill: Instead of accelerating the cup sideways, the handy lever tilts the base of the apparatus so that the cup’s walls are always perpendicular to the fluid’s surface. The device tips when you accelerate it so that the largest force on the cup comes perpendicularly from the base. Now, even when though the fluid has been sloped compared to the horizontal, the cup has been, too! Simply put, the SpillNot prevents spilling by rotating the bottom of the cup so that the sloshing of the fluid never falls over the edge.

Simply put, the SpillNot rotates the bottom of the cup so that the sloshing of the fluid never falls over the edge. Most teachers are familiar with the demonstration of centripetal force that involves a cup or water in the bottom of a bucket is maintained in the bucket even when the bucket is spun in a vertical circle that goes overhead. This is not a difficult demonstration to do, but the SpillNot makes it more fun and students can safely try the experiment themselves. Of course I recommend practicing with clear water first versus using hot coffee. For the most part spilling is nearly impossible unless one goes out of his way to jounce the string. So long as there is tension in the string, spills generally will not happen.

The SpillNot is best for qualitative demonstrations of centripetal force. The idea that it can successfully take an object through a vertical circle so long as its acceleration exceeds the acceleration due to gravity is well demonstrated. But quantitative measurements are technically nuanced and not as convenient. The radius of the circle is often hard to measure and is different for every case of spin. Additionally, the normal force N on the object is not the same as the force acting on the strap. Therefore, one will have to account for the added mass of the apparatus itself if one wishes to measure the force directly; for example by using a spring scale hooked to the loop. Otherwise, one can indeed use the SpillNot to make direct verification of Centripetal Force as being mv2/r.

B A sample procedure for the horizontal circle.

a) Hold the apparatus (loaded with ½ filled cup) out horizontally at an arm’s length
b) Hook a spring scale into the loop of the SpillNot (this can be used to measure m, the mass of the device and cup, and then later to measure the Tension, T)
c) Spin with the device in hand with a sufficient velocity such that the device raises
d) Have a partner time five full cycles with a stop watch, determine t for one cycle
e) During the spin, note the average value of the force on the scale (T)
f) Measure the horizontal radius (if the velocity is sufficient then Rhoriz = R is nearly true, otherwise Rhoriz = R cos θ)
g) Compute the velocity using the formula vcircle = 2πR/t or, more accurately, 2πRhoriz / t
h) Compare T with mv2/R, determine the percent difference, account for experimental error. (One such error is the assumption that either R or T is horizontal or that the mass of the apparatus is all the way out at R, which it is not!) Diagnosing errors is an important skill in physics. Note, that the centripetal force is only caused by Thoriz = T cos θ.

Alternatively, one could use the tilt of the SpillNot to determine the force. This can be accomplished by perhaps taking a picture or still-frame of a person swinging the apparatus. Then, with a protractor, measure the angle at which the rope falls below the horizontal. One can then compare a and v2/R by using tan(Ɵ)=a/g

This lab does not have much to offer pedagogically beyond what a ball on a string can teach, however the device itself is the hook that gets kids interested. It is novel and exciting to be spinning a cup ominously out with the plane of the fluid nearly perpendicular to the floor!

Another lab idea that you might try is the small vertical circle demonstration. In this case the radius is much easier to measure because, for all practical purposes, it is simply the height of the SpillNot plus the small rope. Assuming the cup has a fairly low level, one can determine the minimum speed required to spin the device without spilling. It may be wise and more fun – to do this lab outside. The slowest speed possible will be noticed when, at the top, the cup looses contact with the base. The free body diagram at the top of the spin generates Fnet = mv2/r = N+mg (down or centripetal taken to be positive). The statement “losing contact” implies that there is normal force coming from the base. Thus setting N=0 results in g=v2/r. Measure vcircle = 2πR/t similar to step g in the horizontal circle lab. In this case however I would recommend frame by frame video analysis of a video in which the students spin the device progressively slow until the cup falls off. By counting frames, t can be determined (frame rates can vary from camera to camera). Be careful however, the velocity changes throughout the circle. It will reduce error to use only the top half of the circle. In that case, vsemicircle= πR/t. Post lab analysis might involve comparing g with v2/r and accounting for error; which is usually about 15%.

Despite that the SpillNot does not offer itself easily to quantitative laboratory work, you will be impressed by how easy it is to use. It is not a quantitative demonstration tool. On the contrary, its best use is to demonstrate that the study of physics can be used to solve practical problems in ordinary life. The bonus is that it makes the classic centripetal force demonstrations much easier to perform.

In conclusion, the SpillNot’s ability to demonstrate centripetal force is not unprecedented. Many teachers will already be aware of the demonstration of the “Greek Waiter’s Tray” or water in the bottom of a bucket (both vertical and horizontal circles), and of course loop-the-loop rollercoasters. What is unique about the SpillNot is that you don’t spill whereas spilling is quite common among these other demonstrations, especially when a novice handles the apparatus. A novice, however, can successfully handle the SpillNot. Of course there is always the possibility that students will try to push the limits of the apparatus; but this is not a bad thing! In fact, having students learn what it takes to spill is a good lesson in the scientific method.

James Lincoln

Tarbut V’ Torah High School
Irvine, CA, USA

James Lincoln teaches Physics in Southern California and has won several science video contests and worked on various projects in the past few years.  James has consulted on TV’s “The Big Bang Theory” and WebTV’s “This vs. That”  and  the UCLA Physics Video Project.

Contact: [email protected]

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