Arbor Scientific is providing physics and physical science teachers with a collection of student lab activities for the study of Forces. Here you can browse lab activities by title and get teachers notes, student worksheets and a list of equipment and supplies needed for each activity.

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

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Exploring Newton's First Law: Inertia Kit

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Inertial Balance Set

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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.

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.


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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.


Download Teacher Notes and Student Worksheets.

Required Equipment

Tailgated by a Dart Kit, stopwatch, meterstick, balance

Tailgated by a Dart Kit

SKU: PX-9501
$8.50

Meter Stick 6 pack

In Stock SKU: P1-7072
$18.00

Economy Digital Balance

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$115.00
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Levers and Balance

In the first lab, students will investigate the arrangements of weights that result in equilibrium (balance) in the lever system. They will find that both the force and the distance from the fulcrum are important in evaluating the system. This investigation leads naturally into a study of torque. In the next three labs, students will investigate the three classes of levers, organized according to the arrangement of the input and output forces and the fulcrum. They will compare the levers and determine which class is useful in different situations.

strong>Required Equipment

Physics Workshop Lever Lab, Workshop Stand, Hooked Masses, Spring scales

Download Teacher Notes and Student Worksheets

Lever Lab

In Stock SKU: P4-1600
$55.00

Hooked Mass Set

In Stock SKU: P1-1000
$85.00

Physics Workshop Stand

In Stock SKU: P4-1901
$95.00

Spring Scales (Complete Set)

In Stock SKU: 01-6970
$35.00
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Balloon Helicopter

Newton’s 3rd Law

The balloon helicopter is a classic toy with a simple design. The physics that explains its motion, though, can be difficult to explain. Students will observe the motion of the helicopter and study its construction before applying Newton’s 3rd Law twice to explain how it moves. Newton’s 3rd Law says that every force is opposed by an equal and opposite force. This lab will reinforce the idea that the two forces involved in this law are applied to different objects.

Required Equipment
Balloon Helicopter Kit

Download Teacher Notes and Student Worksheets

Balloon Helicopter Kit

In Stock SKU: P4-2350
$2.95
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Forces in Equilibrium


Students will place three different forces on a washer, and then arrange the forces so that the washer is in stable equilibrium in the center of the table. The forces must be visualized as vectors to understand how they can combine to produce a net force of zero.

Required Equipment
Round table or stool, Table Clamp Pulleys, Spring Scale Set, Hooked Masses, String, and Washer.

Download Teacher Notes and Student Worksheets

Table Clamp Pulley

In Stock SKU: P1-6115
$16.95

Spring Scales (Complete Set)

In Stock SKU: 01-6970
$35.00

Hooked Mass Set

In Stock SKU: P1-1000
$85.00

Roll of String

In Stock SKU: PX-2134
$3.90

The “Small round Table or Stool” required for this lab is probably readily available in your home or classroom. If not you just need a round stable platform that has an edge that will accept the opening of the table clamp pulleys and allow the weights to be suspended without interference of motion. Each lab group would need one table or stool.

The “Washer” required for this lab is readily available at your local hardware or home improvement supply store. Each lab group would need one one washer.

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Life-Size Collisions

Students will observe “explosions,” in which one student on a dynamics cart pushes another. From this, they will confirm the relationship between mass and velocity in determining momentum. They will also reinforce the idea of a closed system by experimenting with which student provides the pushing force. Then a single student on a cart will participate in inelastic and elastic collisions with a thrown weight. Students will observe that a faster throwing speed results in a faster cart speed for both collision types. They will also observe that more force is imparted to the objects in elastic collisions, and make conclusions about technological design based on that observation. 
Required Equipment
Human Dynamics Carts (2), Meter Stick or Measuring Tape, Sandbag or other weight
Download Teacher Notes and Student Worksheets

Human Dynamics Cart

In Stock SKU: P3-3617
$159.00

Meter Stick 6 pack

In Stock SKU: P1-7072
$18.00

 

The “Sandbag or other weight” required for this lab is readily available at your local hardware or building supplies store. One sand bag or weight could be shared among lab groups.

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Circular Motion and the Flying Pig

Pigs Fly

The Flying Pig provides students with a fun way to study circular motion. The pig and its string trace a conical pendulum and allow a perfect opportunity for calculations and measurements of circular motion. Students should be familiar with forces, specifically centripetal force, and how it is calculated. Students should also know the definitions of the fundamental trigonometric functions and how they can be used to find the sizes of parts of a right triangle.

Required Equipment
Flying Pig, Magnetic Ceiling Hooks, Stop Watch, Meter Stick.

Acknowledgements: Thank you to Paul Robinson for his assistance in developing this lab. Paul has taught high school physics since 1974. He is a long-time member of AAPT and is currently Program Chair, Historian, and Section Representative. Paul is also the author of the Conceptual Physics lab manuals.

Download Teacher Notes and Student Worksheets

Flying Pig

In Stock SKU: P4-2165
$9.95

Magnetic Ceiling Hooks

In Stock SKU: P4-2166
$39.00

Digital Stopwatch Timer

In Stock SKU: 52-3200
$9.95

Meter Stick 6 pack

In Stock SKU: P1-7072
$18.00
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Equilibrium and Torque

levers
This lab has two activities. In the first, students investigate the arrangement of masses on a center-pivot lever required to produce balance. They will develop the idea that both force and lever arm produce torque, and that both quantities must be considered when trying to produce equilibrium. Force Vectors are used in diagrams. In the second (advanced) activity, students first use pencil and paper to predict an unknown mass from the arrangement used in the first activity. Then they arrange the lever to its off-center position and experimentally estimate the mass of the lever itself.

Required Equipment Physics Workshop Lever Lab, Workshop Stand, Hooked Masses

Download Teacher Notes and Student Worksheets

Lever Lab

In Stock SKU: P4-1600
$55.00

Hooked Mass Set

In Stock SKU: P1-1000
$85.00

Physics Workshop Stand

In Stock SKU: P4-1901
$95.00
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Collisions on an Air Track

In this lab using an Air Track, students will investigate elastic and inelastic collisions on an air track. Evaluate conservation of momentum and energy.

Required Equipment
Air Track, Timer and Photogates, Meter stick, Balance

Download Teacher Notes and Student Worksheets

Economy Air Track

In Stock SKU: P4-2710
$599.00

Meter Stick 6 pack

In Stock SKU: P1-7072
$18.00

Economy Triple Beam Balance

In Stock SKU: 02-7600
$96.00

Timer and Photogates

In Stock SKU: P4-1450
$279.00
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