How Things Work - Chapter 2 Demonstrations

# Section 2.1 Seesaws

## Demonstration 2.1.1:  A Balanced Stick or Status Exhibits Rotational Inertia

Description: A long stick or statue supported at its center of mass is balanced and obeys Newton's First Law of Rotational Motion.
Purpose: To show that being balanced means experiencing zero net torque, and not necessarily being horizontal or motionless. A balanced object exhibits rotational coasting.
Supplies:
1 Long stick or statue with a hole drilled through its center of mass (a meter-stick with a hole through its center works beautifully). I use a wooden statue of myself that's about a meter tall, made by gluing a color picture of myself to a piece of plywood and then cutting it out with a band or jig saw. Students love seeing Mini-Me go for a spin.
1 Supported shaft that fits reasonably well inside the stick or statue's support hole
Procedure: Support the stick or statueby placing it on the shaft. Show that the stick will remain motionless and horizontal if you start it that way. Since it's not undergoing angular acceleration, it's clearly experiencing zero net torque. Now tilt the stick away from horizontal and show that it still balances—it still experiences zero net torque and doesn't undergo angular acceleration. Finally, spin the stick about the shaft and show that it rotates steadily (neglecting friction and air resistance, which gradually slow it down)—so it still balances.
Explanation: Being balanced means only that an object experiences zero net torque and follows the motion described by Newton's first law of rotational motion. It may or may not be horizontal or motionless. All that you can be sure of is that it will remain motionless if it starts that way and that it will continue to turn steadily if it starts that way.
Demonstration 2.1.2:  Spinning a Supported Ball or Club about Its Center of Mass
Description: Balls and other objects that are supported on a surface tend to spin about their centers of mass.
Purpose: To show that a spinning object naturally rotates about its center of mass.
Supplies:
1 Basketball (or another large symmetric ball)
1 Juggler's club (or another large unsymmetric object)
Procedure: Spin each object on the table to show that it naturally rotates about a special point—its center of mass.
Explanation: The object's center of mass tends to behave inertially: if it starts at rest, it tends to remain at rest. However, if you set the object spinning about that stationary center of mass, it will continue to spin for a long time. It's coasting rotaitonally about its natural pivot.
Demonstration 2.1.3:  Spinning a Falling Ball or Club about Its Center of Mass
Description: Balls and other objects tossed into the air spinning rotate about their centers of mass while their centers of mass fall.
Purpose: To show that an object's motion can often be separated into its center of mass motion (translational motion) and rotation about its center of mass (rotational motion).
Supplies:
1 Basketball (or another large symmetric ball)
1 Juggler's Club (or another large unsymmetric object)
Procedure: Throw each object into the air while spinning to show that it continues to rotate about its center of mass while that center of mass flies through the air like a normal falling object.
Explanation: Gravity effectively acts at the object's center of gravity (which coincides with its center of mass). As a result, the object experiences no torque in flight and continues to rotate freely. At the same time, the object's center of mass falls under the influence of gravity.

## Demonstration 2.1.4:  A Tossed Wobble Ball Spins Crazily about Its Center of Mass

Description: A ball wobbles rapidly back and forth after being thrown upward while spinning.
Purpose: To show that an isolated object rotates about its center of mass.
Supplies:
1 Beach ball (or another inflatable ball)
1 Rubber balloon filled with sand (not stretched)
1 Duct tape
Procedure: Tape the sand-filled balloon firmly to the surface of the inflated beach ball. Now give the ball a spin as you toss it in the air. The ball will wobble wildly back and forth about its center of mass.
Explanation: Putting sand on the ball's surface shifts its overall center of mass toward the sand. When isolated, the ball will no longer rotate about its geometric center—it will rotate about this new center of mass.

## Demonstration 2.1.5:  A Balanced Seesaw Board

Description: A long beam or seesaw board balances when it's supported at its center of mass.
Purpose: To show that being balanced means experiencing zero net torque, and not necessarily being horizontal or motionless.
Supplies:
1 Long beam or board
1 Triangular or cylindrical pivot to support the beam
Procedure: Carefully position the beam on the pivot and adjust the beam's position until it balances. Show that the balanced beam isn't necessary horizontal; it's simply free of any net torque and therefore moves at constant angular velocity.
Explanation: Being balanced means only that an object experiences zero net torque. It may or may not be horizontal or motionless. All that you can be sure of is that it will remain motionless if it starts that way and that it will continue to turn steadily if it starts that way.

## Demonstration 2.1.6:  A Balanced Seesaw Board and One Weight

Description: A single weight added to one end of a balanced seesaw board causes the board to undergo angular acceleration so that the weight-side of the board plummets downward.
Purpose: To show how a force can produce a torque and how that causes angular acceleration.
Supplies:
1 Long beam or board
1 Triangular or cylindrical pivot to support the beam
1 Small weight
Procedure: Balance the empty beam on the pivot. Now place the weight at one end of the beam and watch as the beam undergoes angular acceleration. The heavy side of the beam will soon hit the table or floor. Discuss the fact that the downward push of the weight on the beam produced a torque about the beam's pivot and caused the beam to undergo angular acceleration. Try this experiment with the weight at different distances from the pivot, including directly above the pivot. Show that the torque produced increases as the weight moves farther from the pivot.
Explanation: A force exerted on one end of a balanced seesaw and directed at least partly perpendicular to the lever arm (which lies along the seesaw beam) produces a torque about the pivot and causes the beam to undergo angular acceleration. Moving the weight's downward force farther from the pivot increases the torque and increases the angular acceleration. [Note, however, that the weight's mass also affects the overall rotational mass of the seesaw system, thereby affecting the angular acceleration. This deminstration is cleanest and most convincing when the beam's rotational mass is big and the weight's contribution to rotational mass is insignificant.]

## Demonstration 2.1.7:  Show Angular Acceleration of Different Objects

Description: A bowling ball is much harder to spin than a basketball.
Purpose: To show that an object's angular acceleration depends both on the torque it experiences and on its rotational mass.
Supplies:
1 Bowling ball (or another massive ball)
1 Basketball (or another low-mass ball)
Procedure: Place each ball on the table and give it a spin. Discuss why spinning the more massive ball is harder than spinning the less massive ball, that the more massive ball has the larger rotational mass. Discuss how the strength of the twist (i.e, the magnitude of the torque) affects the ball's angular acceleration. Point out that, overall, the ball's angular acceleration is equal to the torque you exert on it divided by its rotational mass.
Explanation: An object's rotational mass is the measure of its rotational inertia—its resistance to angular acceleration when exposed to a torque. Massive objects usually have large rotational masses, although rotational mass also depends on the spatial distribution of that mass. For example, a pizza is harder to spin about its center than a ball of pizza dough is.

## Demonstration 2.1.8:  A Seesaw Board and Some Weights

Description: Two identical weights make a seesaw board balance when they are equidistant from the seesaw's pivot. Two different weights make the seesaw board balance when their distances from the pivot are inversely proportional to their weights.
Purpose: To show how forces produce torques, how two equal but oppositely directed torques can cancel one another, and how the torque that a force produces is proportional to its distance from the center of rotation.
Supplies:
1 Board (the seesaw board)
1 Pivot (a pencil or a similar rod)
2 Identical weights
1 Weight that is twice as heavy as the others
Procedure: Balance the empty board on the pivot by placing the pivot below the center of the board. Show that the board is balanced—that it experiences no angular acceleration. Now place the identical weights on opposite ends of the board, at equal distances from the pivot. Explain how each weight is exerting a downward force on the board and is thus exerting a torque on the board. Explain that these two torques are in opposite direction about the pivot and thus cancel perfectly so that the board remains balanced. Now replace one of the weights with the heavier weight and show that the balance is spoiled. Finally, move the heavier weight closer to the pivot until the board balances again. Discuss the relationship between force, distance, and torque that allows the heavier weight closer to the pivot to balance with the lighter weight farther from the pivot.
Explanation: Seesaws balance whenever the torques on them cancel perfectly and they experience zero net torque. By placing weights at strategically chosen distance from the pivot, that balance can be achieved.

## Demonstration 2.1.9: Adjusting the Rotational Mass of a Balanced Seesaw

Description: A balanced beam or seesaw becomes more responsive as you move the weights or riders closer to the pivot..
Purpose: To show that the rider's masses contribute to the seesaw beam's overall rotational mass in proportion to the squares of their distances from the pivot. By moving those masses closer to the pivot, you can dramatically reduce the seesaw's overall rotational mass and allow it to respond much faster to torques.
Supplies:
1 Balanced beam on a pivot (or an equivalent seesaw structure).
2 Massive wWeights (or equivalent "riders").
Procedure: Place the two weights on opposite ends of the balanced beam and adjust their positions so that the beam balances. Now exert small torques on the beam with your hand and show how slowly the beam responds (i.e., how small its angular acceleration is). Now move the two weights very close to the pivot and adjust their positions to obtain balance. Now exert small torques on the beam and show how responsive the beam has become. You have clearly reduced its rotational mass greatly.
Explanation: Because the two weights are massive, their contribution to the overall rotational mass of the beam is substantial. When those weights are far from the pivot, the rotational mass is quite big. That's because rotational mass is proportional to the square of distance from the pivot. By moving the weights to the pivot, you reduce their contribution to rotational mass so much that the beam suddenly becomes very responsive to twists and undergoes rapid angular acceleration even when experiencing only modest torques..

## Demonstration 2.1.10:  Two Rods with Equal Masses but Unequal Rotational Masses

Description: Two students try to twist seemingly identical rods back and forth about their middles. One student has far more difficulty than the other.
Purpose: To show just how important the location of mass is in determining an object's rotational mass.
Supplies:
2 Rotational Mass Bars (described below).
2 Students.
Procedure: To make the bars, you'll need two identical hollow aluminum pipes about 1 meter long and 3 cm in diameter, with relatively thin walls and therefore relatively little intrinsic rotational mass. You'll also need two pairs of identical masses to glue inside those pipes. In one pipe, glue the pair of masses just inside the pipe's ends: one mass at each end. In the other pipe, glue the pair of masses inside the middle of the pipe. Finally, cap all four pipe ends so that no one can see what's inside the finished rods. During class, have two students come up front and let each one hold the pair of rods without shaking them. The students should recognize that these rods have equal weights and therefore equal masses. Then let each student hold only one of the rods at its center and, at the count of three, begin twisting the rods back and forth as rapidly as possible. The students will twist the rods at unequal paces. The student with the rod having its mass at its ends will find the rod very unresponsive. It will experience only modest angular accelerations in response to large torques.
Explanation: By putting all the rod's mass in its ends, you produce a rod with a huge rotational mass. In contrast, by putting the other rod's mass in its middle, you produce a rod with a very small rotational mass. The two rods then experience very different angular accelerations in response to roughly equal torques.

## Demonstration 2.1.11: A One-Meter Stick and a Two-Meter Stick Tip Over at Different Rates

Description: A one-meter stick and a two-meter stick are leaned to equal angles and then released. The one-meter stick falls over and hits the floor first.
Purpose: To show that while the two-meter stick experiences four times as much gravitational torque as the one-meter stick, the two-meter stick has eight times as much rotational mass as the one-meter stick and therefore tips over more slowly than the one-meter stick.
Supplies:
1 One-meter stick (or equivalent)
1 Two-meter stick (or equivalent)
Procedure: Hold the two sticks almost vertically on the floor or a large table. Let them lean out to equal angles. Ask the students to predict which stick will hit the floor or table first when you release them. Then release them and watch the one-meter stick hit the floor or table first.
Explanation: The longer stick experiences four times the gravitational torque because it has twice the weight and that weight is located at twice the average distance from the pivot (two times two is four). But the longer stick has eight times the rotational mass because it has twice the mass located an average of twice as far from the pivot and that distance from the pivot gets squared in calculating rotational mass (two times two-squared is eight). So the longer stick has four times the torque but eight times the rotational mass and undergoes only half the angular acceleration of the short stick. The short stick hits the floor or table first.

## Demonstration 2.1.12:  Flinging an Apple with a Stick

Description: An apple is skewered on a stick and then flung at enormous speed by swinging the stick.
Purpose: To show that a lever can help you accelerate a relatively low-mass object (the apple) to enormous speeds.
Supplies:
1 Apple (rather firm, so that it grips the stick well)
1 Stick (a sturdy elastic stick about 1 to 1.5 m long)
Procedure: Sharpen the end of the stick so that it can pierce the apple without splitting the apple. With the apple firmly attached to the stick, swing the stick very rapidly over your head. When the apple is just about directly overhead, snap the stick downward to pull it out of the apple and the apple will continue forward at tremendous speed. Try this outside in a safe area first because it takes some practice (it helps to have an old apple tree with lots of apples on the ground beneath it). If you choose to do it inside, be careful not to hit anyone or break anything. In my lecture hall, I can fling the apple against a cement wall so that clean-up is relatively easy. But sometimes I miss…
Explanation: The maximum speed at which you can throw an apple is determined largely by the speed at which you can move your arm. The apple's mass is almost insignificant. By putting the apple at the end of a stick, you can accelerate the apple to a much higher speed because you don't have to accelerate your arm to that speed.

## Demonstration 2.1.13:  Breaking an Egg on a Seesaw

Description: An egg sits on one side of a small seesaw and you strike the other side of the seesaw with a mallet. The egg explodes in place.
Purpose: To show that a large unbalanced torque causes rapid angular acceleration and that a large force exerted on the surface of an egg will break that egg.
Supplies:
1 Egg
1 Small seesaw (a short, sturdy board will do as the seesaw board and a pencil will do as the pivot)
1 Mallet (or even a book)
Procedure: Place the egg on one side of the seesaw. You may need to prop it in place so that it doesn't roll off. Ask the students whether the egg will rise up into the air and then smash when it lands or whether the egg will shatter during the launching process. Now strike the other side of the seesaw firmly with the mallet. The egg will explode without rising.
Explanation: When you hit the seesaw board, it experiences a large unbalanced torque and undergoes rapid angular acceleration. The egg, with its inertia, exerts a torque in the opposite direction but can't stop the angular acceleration from occurring. The seesaw board rotates rapidly into the egg, smashing it.

# Section 2.2 Wheels

Demonstration 2.2.1:  A Box Experiences Static Friction and Sliding Friction
Description: A box at rest resists sliding and, when actively sliding, skids to a stop. When pulled with a spring scale, itinitially resists sliding but eventually slides forward.
Purpose: To illustrate the forces of static and sliding friction, and their oppositions to relative motion between two surfaces.
Supplies:
1 Box (or a heavy block)
1 String
1 Spring scale
1 Smooth surface
1 Rough surface
Procedure: First show that the box remains at rest on the table, even if you push it gently toward one side. Discuss static friction. Then push harder and show that the box begins to move but that it doesn't accelerate indefinitely, even though you keep pushing. Finally, stop pushing and show that it coasts to a stop. Discuss sliding friction. Use the string to attach the spring scale to the box and show that the force of static friction can range from zero up to some maximum value, depending on how hard you pull the box to one side. Then start the box moving and show that the force of sliding friction is just about constant, no matter how fast you move the box (as long as you move it at constant velocity). Now add weight to the box and show that the frictional forces can become stronger—discuss the microscopic basis of friction. Finally, try sliding the box across different surfaces to show that surface roughness also affects the frictional forces.
Explanation: Static friction opposes any relative motion between two surfaces that are at rest with respect to one another. Sliding friction opposes relative motion between two surfaces that are already sliding across one another. Since these two forces are caused by "collisions" between microscopic features of the two surfaces, pushing those surfaces together more strongly increases the frictional forces.

## Demonstration 2.2.2:  Using Sliding Friction to Wear Away a Piece of Wood

Description: A piece of light wood quickly vanishes when rubbed against a sheet of coarse sandpaper.
Purpose: To show that sliding friction causes wear.
Supplies:
1 Piece of soft wood, ideally balsa wood.
1 Sheet of coarse sandpaper
Procedure: Lay the sandpaper on a table and hold the wood against it. Show first that static friction causes no wear and can oppose the start of relative motion between the wood and paper forever. Now begin to slide the wood rapidly back and forth across the paper and watch the wood disappear into sawdust. Discuss that sliding friction does cause wear and that it is wear that is reducing the wood to tiny pieces.
Explanation: Sanding is the deliberate use of sliding friction to wear away a material. In this case, the sandpaper is wearing away the wood. If the wood is soft enough and thin enough, it will vanish in a matter of seconds..

## Demonstration 2.2.3:  Using Sliding Friction to Start a Fire

Description: A wooden peg is turned rapidly with a bow. Friction between the peg and a board causes them to heat up and begin smoking.
Purpose: To show that sliding friction converts work into thermal energy.
Supplies:
1 Wooden peg, about 1 cm in diameter and about 10 cm long. Sharpen it at both ends as though it were a pencil.
1 Bow (either a commercial bow from an archery set, or an equivalent homemade one)
1 Wooden block with a hollow greased socket for the peg end
1 Wooden board with an ungreased hole for the peg's other end
1 Clamp
Procedure: Clamp the board to the table. Wrap the bow string once around the peg and insert the peg in the holes of the block and baord. Press the block down so that the peg is held tightly between the block and board and move the bow back and forth fairly rapidly. The peg should spin one way and then the other as you move the bow. If you apply the right amount of pressure to the peg and move the bow quickly enough, sliding friction between the peg and the board will cause them to heat up and smoke. While I have never been able to start a fire this way, it should be possible with the help of some dry tinder or cotton balls.
Explanation: As the peg turns in its hole, the two surfaces slide across one another. They convert the work that you are doing by pushing and pulling on the bow into thermal energy.
Follow-up: Light a match and discuss the role of sliding friction in the ignition process. Have the students rub their hands together until their skin feels warm. They should be aware that they are doing work against sliding friction as they move their hands.

## Demonstration 2.2.4:  Forms of Energy

Description: A number of objects are shown to contain energy.
Purpose: To show that energy, the capacity to do work, can take many forms.
Supplies:
1 Ball
1 Wound or compressed spring (I use a trick can of nuts, which contains a springy toy snake)
1 Elastic balloon, uninflated
2 Magnets
1 Capacitor and charging system (see next demo)
1 Battery and light bulb
1 Pretend stick of dynamite
Procedure: This demonstration collection is simply meant to illustrate that energy takes many different form. In each case, it's helpful to show that the energy really is the capacity to do work and that the kinetic or potential energy can cause some work to be done. Use the ball to show that kinetic energy can do work on a target. Use the ball to show that gravitational potential energy can do work on another object. Inflate the balloon and let it fly around the room. Let the magnets jump apart (or together). Use the capacitor to make a loud spark. Use the battery and light bulb to make electric charges move and heat the bulb's filament white hot. And talk about the pretend dynamite.
Explanation: Energy is the capacity to do work and it can take many different forms.

## Demonstration 2.2.5:  Forms of Energy - Electrostatic Potential Energy

Description: A large capacitor is charged with the help of a string of 9V batteries (or a power supply). It is then discharged with a screwdriver, producing a large spark and a loud pop.
Purpose: To show one of many forms of energy.
Supplies:
1 Large electrolytic capacitor (at least 10,000 µF with a rated voltage of about 75 V; for electrical safety reasons, don't use voltages greater than 75 V and be careful even with 75 V!)
1 String of 9V batteries with a total voltage of no more than the rated voltage of the capacitor. Form the string by clipping the negative terminal of one to the positive terminal of another, and so on.
2 Wires
1 Old screwdriver
Safety glasses
Procedure: Connect the string of batteries to the capacitor, positive end to positive end and negative end to negative end. The batteries will begin to transfer charge from one side of the capacitor to the other, a process that will take a few seconds for new batteries but may take as long as a minute for old batteries. If you want to know how the transfer is progressing, measure the voltage drop across the capacitor with a voltage meter. Be careful, because both the string of batteries and the capacitor have enough voltage to injure you.
Once the capacitor is fully charged, detach the batteries. Now discharge the capacitor by connecting its two terminals with the screwdriver. You should wear goggles or safety glasses while doing this and be prepared for a big spark. Since the discharge will blow chunks of metal out of both the screwdriver and the capacitor's terminals, you should probably extend the capacitor's terminals with bolts if you want to be able to do this demonstration more than a couple of times. This demonstration drains the batteries substantially, so you won't be able to do it more than a few dozen times before you'll have to replace the batteries.
Explanation: The batteries pump charge from one side of the capacitor to the other. One side of the capacitor acquires a positive charge and the other side acquires a negative charge. The attractive forces between these two opposite charges are capable of doing a substantial amount of work. They have electrostatic potential energy. When you connect the two sides of the capacitor with the screwdriver, the charges move toward one another and release their stored energy as heat, light, and sound.
Demonstration 2.2.6:  A Swinging Pendulum
Description: A pendulum swings back and forth, with its energy transforming from gravitational potential energy to kinetic energy and back again, over and over.
Purpose: To show the conversion of energy from one form to another.
Supplies:
1 Pendulum (or any large object supported by as long a string as is practical)
Procedure: Start the pendulum from rest by pulling it back and letting it go. Point out that you do work on it by pulling it away from its central position and thus give it its initial energy. As it swings back and forth, note the times at which its energy is all gravitational (at the end of each swing) and all kinetic (at the bottom of each swing). To make it swing harder, push it every time it begins to swing away from you—you are doing work on it. To make it swing less hard, push it every time it begins to swing toward you—it's doing work on you.
Explanation: The pendulum has two forms for its energy: gravitational potential energy and kinetic energy. It naturally transforms its energy from one form to another as it swings. You can add energy to it by doing work on it once each cycle or you can take energy out of it by having it do work on you once each cycle.

## Demonstration 2.2.7:  Pushing a Swinging Pendulum

Description: Pushing on a swing can make the swing move more or less, depending on when the push occurs in the swing.
Purpose: To show that energy is transferred by doing work.
Supplies:
1 Pendulum (a ball on a string, or something equivalent)
Procedure: Give the pendulum a series of pushes. Time the pushes so that they always occur as the pendulum moves away from you—so that you do work on it. The pendulum should swing more and more. Now repeat the pushes, but time them so that they always occur as the pendulum moves toward you—so that it does work on you. The pendulum should swing less and less.
Explanation: Making a swing travel further requires that you transfer energy to it. You do this by pushing it as it moves away from you—so that the push and the distance the swing travels are in the same direction. Making the swing travel less far requires that it transfer energy to you. You do this by pushing it as it moves toward you—so that the push and the distance it travels are in opposite directions.
Follow-up: Discuss how this applies to pushing a child on a swing.

## Demonstration 2.2.8:  Mixing and Unmixing Black and White Beans

Description: A platter containing black beans on one side and white beans on the other is mixed by a student with her eyes closed. The result, not surprisingly, is a relatively random mixture. She then closes her eyes again and tries to unmix the beans. The result, still not surprising, is another random mixture.
Purpose: To show that disordering a system is far easier than ordering it and that disordering energy (converting useful work into relatively useless thermal energy) is far easier than the reverse.
Supplies:
1 Platter or dish
1 Cup of dried black beans
1 Cup of dried white beans
1 Student
Procedure: Carefully pour the black beans on one side of the platter and the white beans on the other side. Now have a student close her eyes and stir the beans together. After a little while, have her stop and open her eyes. Everyone should note that the beans are now scrammbled. Have her close her eyes and stir the beans again, perhaps stirring backwards in hopes of unmixing the beans perfectly. Note as she stirs that the laws of motion are silent on the matter of unmixing and that there is not mechanical reason why she shouldn't be able to perfectly separate the black beans from the white beans. Now have her stop and open her eyes. The beans will still be mixed. In fact, no matter how many times she tries to unmix the beans, she'll never succeed. It's just too unlikely.
Explanation: While mixing and unmixing the beans both fall within the motions permitted by the laws of motion, the laws of statistics frown on the possibility of unmixing the beans by pure random chance. It's just too unlikely. In general, highly ordered situations are fragile and their order is easily lost to random processes. In this case, the separated black and white beans were a highly ordered system and their order was destroyed by random stirring. Recovering that order through additional random stirring is so unlikely that it is effectively impossible.

## Demonstration 2.2.9:  A Box and Rollers

Description: A box that slides badly on the table, coasts almost freely when it's supported by rollers.
Purpose: To show that rollers eliminate sliding friction.
Supplies:
1 Heavy box (or a large heavy block)
3 Dowels (or equivalent rods)
Procedure: Place the box directly on the table and give it a push. Show that it quickly slows to a stop as sliding friction exerts a force on it in the direction opposite its motion. Now support the box on two rollers and place the third roller in front of it. Push the box toward the third roller and show that it coasts smoothly forward as long as it doesn't fall off the rollers. Discuss the fact that the only friction left in the situation is static friction.
Explanation: As the rollers turn, their surfaces don't slide across those of the box or table. As a result, there is only static friction present and nothing converts the box's kinetic energy into thermal energy. The box thus coasts forward indefinitely after you give it a push.

## Demonstration 2.2.10:  Wheels - Free and Powered

Description: A freely turning wheel spins as you pull it across the table. A turning (powered) wheel pushes itself forward across the table.
Purpose: To show that static friction between the ground and the bottom of a wheel can either cause the wheel to turn (in the case of a freely turning wheel) or can propel the wheel across the ground (in the case of a powered wheel).
Supplies:
1 Bicycle wheel (or a similar wheel on an axle)
Procedure: Hold the bicycle wheel against the table and begin rolling the wheel across the table. Point out that it is static friction between the table and the wheel that is producing the torque that makes the wheel turn. Now hold the bicycle wheel against the table and begin to twist the wheel with your hand. As the wheel begins to rotate, it will also propel itself across the table. Point out that it is static friction between the table and the wheel that is allowing the wheel's rotation to produce the forward force that propels the wheel forward.
Explanation: The forces of static friction between the table and the wheel affect both the wheel's center of mass motion (its progress forward or backward across the table) and its rotational motion (how it spins).
Follow-up: Show that when a wheel skids, sliding friction appears and some energy is converted to thermal energy.

## Demonstration 2.2.11:  Roller or Ball Bearings

Description: The balls or rollers in a bearing rotate as the inner part of the bearing turns relative to the outer part.
Purpose: To show that the balls or rollers in a bearing experience only static friction—they touch and release as they move past the surfaces. There is no sliding friction in a ball or roller bearing.
Supplies:
1 Large ball or roller bearing without aprons (that would cover the internal components)
Procedure: Show that the balls or rollers in the bear touch and release the surfaces of the bearing as the inner and outer surfaces move relative to one another.
Explanation: The balls or rollers in the bearing are equivalent to rollers places between the inner and outer surfaces of the bearing. The balls or rollers move slowly around the inner surface as the two surfaces moves relative to one another. Because the balls or rollers never slide across the surfaces, there is no sliding friction and no energy wasted as thermal energy.

## Demonstration 2.2.12:  A Skidding Wheel Wastes Energy

Description: A spinning grinding wheel makes sparks as it "skids" on a steel surface.
Purpose: To show that a skidding wheel uses sliding friction to turn useful energy into thermal energy.
Supplies:
1 Grinding wheel on an axle
1 Electric drill
1 Steel plate
1 Clamp to hold the metal plate to the table
Procedure: Clamp the steel plate to the table. Put the grinding wheel in the drill and start the wheel spinning fairly rapidly. Now touch the wheel to the steel plate and watch the sparks fly. (Alternatively, you can use a bench grinder and hold the steel yourself.)
Explanation: As the grinding wheel slides across the plate, it wears steel away from the plate's surface and ejects the hot wear chips into the air, where they burn up.

# Section 2.3 Bumper Cars

## Demonstration 2.3.1:  Play with Momentum while Riding a Cart

Description: You coast back and forth across the room, acquiring momentum from the ground, wall, or a student and then carrying that momentum across the room before depositing in the floor, wall, or another student.
Purpose: To demonstrate conservation of momentum and show that it is a quantity of motion that you can acquire, carry with you, and then give away.
Supplies:
1 Cart with low-friction wheels and bearings
Procedure: Stand or sit on the cart and then acquire some momentum in a direction that the cart can roll. You can acquire this momentum by pushing on the floor or wall, or by pushing against a student helper. Carry the momentum with you as you coast across the room and then give away the momentum to the floor, wall, or another student. Do this repeatedly until everyone become convinced that you are acquiring, carrying, and then giving away momentum. They should also begin to recognize that momentum has a direction and that acquiring leftward momentum is the opposite of acquiring rightward momentum.
Explanation: Since momentum is conserved, this demonstration is simply showing that conservation. As long as the students can see each time momentum is transferred, they'll begin to understand that it is a conserved quantity of motion that you can carry with you or exchange with other things.

## Demonstration 2.3.2:  Momentum Transfers on an Air Track

Description: You slide an airtrack car along an airtrack and it collides into another identical but stopped car. The second car picks up the motion and the first car stops. A similar collision between cars with different masses results in a more complicated transfer of motion.
Purpose: To show the transfers of momentum that occur during collisions.
Supplies:
1 Airtrack
2 Airtrack cars with equal masses and elastic bumpers
2 Airtrack cars with unequal masses and elastic bumpers
Procedure: Turn on the airtrack and slide one car along its surface. Note each time you give the car momentum, when it is coasting along with that momentum, and when you remove the momentum. You may want to discuss what happens to the car's momentum during bounces off the track ends. Now slide the first car toward an identical but stopped car and watch as the first car transfers essentially all of its momentum to the second car. It will be relatively easy to see that some directed quantity of motion (i.e., momentum) has passed from the first car to the second. Do the same thing in the opposite direction to highlight the fact that momentum has a direction. Now play with collisions between cars of unequal mass to show how the transfers of momentum have different effects on the velocities of cars of unequal mass.
Explanation: Since momentum is conserved, you are simply showing how it is carried by the airtrack cars and transferred between them.
Follow-Up: You can do these same experiments on a grand scale using students on carts. If two students with equal masses collide and push off one another carefully, they can transfer momentum just like the two identical airtrack cars. If two students with very different masses collide and push off one another carefully, the low-mass student will experience a much larger overall change in velocity.
Follow-Up: There is a classic toy, often called the "executive toy", that has a set of metal balls hanging in a straight line. If you pull one of the balls outward and let it swing into the others, the far ball will pop outward. Momentum flows through the line from the arriving ball to the leaving ball. A similar effect occurs in a chain of coins when you slide a coin into the end of the chain. Trapping the chain between two rulers makes it easy to hit the end of the chain.

## Demonstration 2.3.3:  Throwing an Object—Momentum Conservation

Description: You sit on a cart at rest and throw a heavy object. While the object accelerates in one direction, you accelerate in the other.
Purpose: To demonstrate the transfer of momentum and to show that momentum is conserved.
Supplies:
1 Cart with low-friction wheels and bearings
1 Heavy (but soft) object
Procedure: Sit on the cart with the heavy object in your lap. The cart should be at rest on a smooth level surface. Now throw the object as hard as possible along a direction that the cart can roll. The cart will begin rolling in the opposite direction, with you still on it.
Explanation: At the start of the demonstration, you and the object have zero total momentum. As you throw the object, you transfer momentum to it in one direction and thus end up with an equal amount of momentum in the opposite direction. Overall, the momentum is still zero, but now the object has momentum in one direction and you and the cart have momentum in the opposite direction.

## Demonstration 2.3.4:  Play with Angular Momentum while Sitting on a Swivel Chair

Description: You coast rotationally on a swivel chair, acquiring angular momentum from the ground, wall, or a student and then carrying that angular momentum as you spin before depositing in the floor, wall, or the student.
Purpose: To demonstrate conservation of angular momentum and show that it is a quantity of motion that you can acquire, carry with you as you turn, and then give away.
Supplies:
1 Swivel chair with low-friction bearings
Procedure: Stand on the swivel chair and then acquire some angular momentum up or down. You can acquire this angular momentum by exerting a torque on the floor or wall, or by exerting a torque on a student helper. Carry the angular momentum with you as you spin and then give away the angular momentum to the floor, wall, or the student. Do this repeatedly until everyone become convinced that you are acquiring, carrying, and then giving away angular momentum. They should also begin to recognize that angular momentum has a direction and that acquiring upward angular momentum is the opposite of acquiring downward angular momentum.
Explanation: Since momentum is conserved, this demonstration is simply showing that conservation. As long as the students can see each time momentum is transferred, they'll begin to understand that it is a conserved quantity of motion that you can carry with you or exchange with other things.

## Demonstration 2.3.5:  Twisting a Wheel—Angular Momentum Conservation

Description: A student sits on a swivel chair and turns over a spinning bicycle wheel. When he/she reverses the wheel's direction of rotation, he/she and the swivel chair also experience a change in rotation.
Purpose: To demonstrate the transfer of angular momentum and to show that angular momentum is conserved.
Supplies:
1 Bicycle wheel with handles attached to the axle (Inserting metal wire into the tire helps by adding mass to the rim and increasing the wheel's rotational mass.)
1 Swivel chair with a low-friction rotational bearing
1 Student
Procedure: Get the bicycle wheel spinning as rapidly as possible with your hands or with a motor. We use a bench grinder with a polishing wheel replacing its grinding wheel—pressing the bicycle wheel against the spinning polishing wheel gets the bicycle wheel spinning quite rapidly after about 10 or 20 seconds. Now twist the bicycle wheel so that it's spinning horizontally, with its axis of rotation pointing upward (it spins counter-clockwise as viewed from above). Have the student sit on the swivel chair and hand him/her the spinning wheel. Point out that the wheel now has all the angular momentum and that that angular momentum is upward. Now have the student lift his/her feet off the ground and flip the bicycle wheel upside down, so that it's axis of rotation points downward. The student will begin to spin with his/her axis of rotation upward. The wheel has transferred twice its upward angular momentum to the student and now has an equal amount of downward angular momentum. When the student flips the wheel back to its original situation, the student will stop spinning. The wheel will now have its original upward angular momentum again.
Explanation: Each time the student flips the bicycle wheel, he/she is exerting a torque on it and it is exerting a torque on the student. When the student turns the wheel over, its angular momentum reverses and the student end up with twice the wheel's original angular momentum. Overall, the angular momentum remains the same, but it's distributed differently.

## Demonstration 2.3.6:  A Diablo—Angular Momentum Conservation

Description: You spin a diablo (an hourglass-shaped rubber toy) on its string support and show that, once spinning, it tends to continue spinning steadily about a fixed axis in space.
Purpose: To show that angular momentum is conserved.
Supplies:
1 Diablo—an hourglass-shaped rubber toy with a narrow metal waist. This toy is supported from a string that stretches between two sticks.
Procedure: Rest the diablo on the string and begin to snap one of the sticks in a series of quick upward jerks. The string will grab onto the diablo during those jerks and exert a torque on it to start it spinning. Keeping the diablo level requires that you pay attention to the relative positions of the stick ends. It takes some practice to get the diablo to spin smoothly and horizontally. However, once it's spinning nicely, you can walk around it, holding it up by the strings, and it will spin about a fixed axis in space for a long time.
Explanation: The spinning diablo is virtually free from external torques, so its angular momentum doesn't change as you walk around it.

## Demonstration 2.3.7:  Changing Your Rotational Mass

Description: You spin on a swivel chair with your arms outstretched and weights in your hands. As you pull your hands inward, you begin to spin faster and faster.
Purpose: To show that because angular momentum is conserved, a spinning object that reduces its rotational mass must spin faster.
Supplies: