# Labs

Arbor Scientific introduces a growing collection of science labs, activities and experiments for physics and physical science teachers. Science labs are designed to cover important key concepts, and may be downloaded and used in your classroom. Whether you’re a teacher or home schooling parent, these labs are designed for you.

Science labs include teacher’s notes with a brief concept review, tips, applicable National Science Content Standards, and a list of equipment. The student pages are ready to reproduce and use right away.

## 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.

# Recommended Tools

## Rotational Inertia Demonstrator

In Stock SKU: P3-3545
\$185.00

## Exploring Newton's First Law: Inertia Kit

In Stock SKU: P6-7900
\$67.00

## Inertial Balance Set

In Stock SKU: P4-1051
\$32.00

## 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.

## Forces On Inclined Plane Demonstrator

In Stock SKU: P4-1420
\$69.00

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.

## Momentum – Tailgated by a Dart

In this lab, students will learn to estimate the speed of an object by applying conservation of momentum to an inelastic collision. Energy is not lost its transferred from one object to another. Students will fire a dart into the back of the free rolling car and measure the distance of the car, calculate the speed of the dart and car, and measure the mass of the car and dart.

### Required Equipment

Tailgated by a Dart Kit, stopwatch, meterstick, balance

SKU: PX-9501
\$8.50

## Meter Stick 6 pack

In Stock SKU: P1-7072
\$18.00

## Economy Digital Balance

In Stock SKU: 02-7000
\$115.00

## Density Rods

The Density Rod Set consists of two rods. The aluminum rod sinks in warm water and floats in cool. This is because cool water is more dense than warm, and the aluminum rod is made to be between those two densities. The PVC rod does the reverse – floats in warm water and sinks in cool. This time, the rod changes more than the water, becoming more dense when it is cool.

Required Equipment
Balance, Film Canisters, Pennies, Tape

## Density Rod Set

In Stock SKU: P1-1020
\$20.00

## 100 ml Polypropylene Cylinder

In Stock SKU: 06-3043
\$4.00

## Student Thermometer

In Stock SKU: 68-6202
\$3.75

The “food coloring and rubbing alcohol” required for this lab is readily available at grocery store. Each lab group would need one container of each.

## Quantum Lab (Inquiry)

Indirect Measurement Lab

Something that is quantized exists in multiples of a set quantity. Examples are charge [1.6 x 10-19C] or quantum energies of photons. Planck and Einstein predicted that light existed as discrete bundles called photons. Since they could not see a unit of photon energy, this lab constructs a model of how quanta was derived and visualized by scientists. In this INQUIRY lab, students will develop their own method for finding the pennies’ mass.

Required Equipment
Balance, Film Canisters, Pennies, Tape

## Sartorius M-Prove Model AY511 510g X 0.1g

In Stock SKU: 02-7069
\$179.00

The Film Canister required for this lab is readily available here

The “Tape” required for this lab is readily available at your office or school supply store. Each lab group would need one roll or access to a roll.

## Quantum Lab

Quantum Measurement Lab

Something that is quantized exists in multiples of a set quantity. Examples are charge [1.6 x 10-19C] or quantum energies of photons. Planck and Einstein predicted that light existed as discrete bundles called photons. Since they could not see a unit of photon energy, this lab constructs a model of how quanta was derived and visualized by scientists.

Required Equipment
Balance, Film Canisters, Pennies, Tape

The “Tape” required for this lab is readily available at your office or school supply store. Each lab group would need one roll or access to a roll.

## Sartorius M-Prove Model AY511 510g X 0.1g

In Stock SKU: 02-7069
\$179.00

## Picture of a Lab: Different Graph Types

Picture of a Lab – Different Graph Types

Station #1 investigates the relationship between force and displacement of a stretched spring. Students will discover a direct linear relationship, with an equation of the form y = mx + b. Station #2 demonstrates Boyle’s Law, or the relationship between the pressure on a gas and its volume. The graph is a hyperbola, y = 1/x. Station #3 relates light intensity to distance from the source. The graph shows an inverse-square relationship, with an equation y = 1/x2. Station #4 uses staggered, stacked blocks to result in a simple parabolic graph, where y = x2.

Required Equipment
Hooked Masses, Meter Stick, Motion Sensor, D-Cell Holder, D-Cell Battery, 2 Alligator Wires, Mini Bulb Holder, Mini Bulb, light sensor, Data-logger, Spring Set/3, Computer with Excel or other graphing application, Several identical weights or books, 7 wood blocks

Acknowledgements: Thank you to Dwight “Buzz” Putnam for his assistance in developing this lab. Buzz is a 25 year veteran physics teacher at Whitesboro High School, New York Science Teacher of the Year and Host of the Regents Physics Answers television show on PBS. You can also find him refereeing high school basketball games as well as presenting at the NSTA National Conferences.

## Hooked Mass Set

In Stock SKU: P1-1000
\$85.00

## Go! Motion Sensor

In Stock SKU: P4-2400
\$119.00

## D-Cell Battery Holder

In Stock SKU: P6-1400
\$2.25

## C Battery

In Stock SKU: 44-1091
\$1.50

## Alligator Leads (Pack of 10)

In Stock SKU: P4-3000
\$4.50

## Miniature Bulb Base

In Stock SKU: P6-1401
\$1.50

## 3.2V Miniature Bulbs 10 Pack

In Stock SKU: P6-1407
\$5.50

## Spring Set, 3 Different Sizes

In Stock SKU: PX-2120
\$5.95

The “Computer with Excel or other graphing application” required for this lab is any computer that you may have that has software capable of plotting graphs. In order to use the data logger in this experiment, the computer would need to be of PC version (Windows).

The “Several identical weights or books” required for this lab are any objects that you may have or that can also be purchased from your local convenience or hardware store that are identical in weight.

The “wood blocks” required for this lab can be cut from any lumber that you may have or purchased from your local building supply store. The blocks should all be identical in measurements.

## Density of a Solid

Regular and irregular objects will be used. Students will devise a way of finding the volume of each object – calculating the volume of a cube or using water displacement for irregular objects. They will calculate the density of each and compare to standard values.

Required Equipment

Density Blocks, Balance, Graduated Cylinder, Various objects.

## Assorted Density Block Set

In Stock SKU: P1-1010
\$23.00

## Sartorius M-Prove Model AY511 510g X 0.1g

In Stock SKU: 02-7069
\$179.00

The “Various objects” required for this lab are any small irregular solid objects that you would like to calculate the density for as a part of this experiment.

## Acceleration Force and Mass

 Students love fast moving experiments, but higher speeds often require higher technology. That can challenge the budget and students’ ability to use the technology. These simple, but highly accurate photogates remove both barriers. No costly computers are needed, and set up is easy. Students literally ‘get up to speed’ fast! Stephen Rea has been teaching physics and honors physics at both the high school and college level since 1980. Currently at the University of Michigan, Dearborn, he was the Michigan State Science Teacher of the year in 1994. Using the Timer & Photogates in the Classroom! Arbor Scientific’s photogates are highly effective for use in multiple experiments, including measuring acceleration and exploring projectile motion and Conservation of Momentum. Here are two examples: Acceleration: The Timer & Photogate system is perfect for measuring the acceleration of an object. This typically requires students to measure the time for the object to pass through each of the two photogates, plus the time to travel between them. The way that these values are displayed on the timer makes it easy for students to capture the data. Conservation of Momentum: Experiments with Conservation of Momentum typically involve determining the speeds of two colliding objects, both before and after the collision. Using the timer memory feature, students can use the photogate system to obtain all four time values with precise accuracy. As an example of how they can be used, the teacher challenges students to use the photo-timer system with gliders on an air track and come up with an experiment that confirms Conservation of Momentum. Required Equipment Timer & Photogates 2.0, and the Car& Ramp Recommended quantity per lab group: 1 Timer & Photogates 2.0 P4-1450 Digital Timer & photogates. No computer required for this simple, intuitive data collection device. Complete set includes Timer, two photogates with cords, AC adaptor, user’s manual, and hard carrying case. Click here to get it >> Recommended quantity per lab group: 1 Car & Ramp 2.0 Lab P4-1405 Experiment with distance, time, velocity and acceleration, Newton’s laws and simple machines. The 120cm ramp attaches to the Workshop Stand at angles up to 65°. Click here to get it >>

## Tornado in a Bottle Inquiry

We will use funnels, soda bottles, and a toy called a Tornado Tube to explore the concepts of moment of inertia, rotational motion, angular momentum, kinetic and potential energy, and air pressure in an attempt to discover and explain the physics of a rather complex hydrodynamic system.

Required Equipment
Plastic Funnel, Stopwatch, Vortex Tube, Materials for Designing a Funnel, 2 Empty Soda Bottles, Water Source, Large Tub or Sink.

Acknowledgements: Thank you to Dr. J.R. Harkay author ofPhenomenal Physics for providing this student inquiry activity.Adapted from “Twister! Tornado in a Bottle,” an Inquiry Exercise by J. R. Harkay. See www.PhenomenalPhysics.com for more information on the complete Guided Inquiry Curriculum.

Dr. Russell Harkay
Keene State College
New Hampshire