1A10 - Basic Units

Dubious Clocks Two large "clocks" without numbers mounted on the same vertical board. The clocks coincide at zero on each revolution, but differ in their readings elsewhere around the circle. The difference is subtle enough to encourage doubt as to which is "correct." Shows that timing devices can be useful for some measurements but worthless for others.

1A20 - Error and Accuracy

Calipers and Micrometers (1A20.41) Vernier and digital calipers, and micrometers.

1A30 - Coordinate Systems

Chalkboard Globe (1A30.40) A large globe surfaced with a black material that can be written on with chalk. Can be used to draw and discuss polar coordinates.

Acrylic Globe Clear plastic globe has lines of latitude and longitude drawn on it for discussion of polar coordinate systems.

1A40 - Vectors

Vector in Coordinate Frame (1A40.10) A three dimensional stick-and-ball coordinate frame has a vector arrow emerging from the origin that can be adjusted to any angle within the frame.

Sum Vector (1A40.31) A pair of acrylic vector arrows make up two sides of a parallelogram, with a tape measure "vector" extending diagonally across the parallelogram to represent the sum of the vectors. Change the angle between the vectors and the length of the sum vector changes in accordance with the parallelogram rule.

1A50 - Math Topics

Radian Disc (1A50.10) A large disc marked off in radians, with a flexible strip of length r to show the derivation of the unit.

1A60 - Scaling

"Powers of Ten" (1977) (1A60.10) A ten minute video which uses the notion of powers of ten to compare the relative sizes of objects in the universe, from clusters of galaxies to individual protons.

1C10 - Velocity

1C20 - Uniform Acceleration

Guinea and Feather (1C20.10) Two transparent tubes contain paper and an aluminum disc. Times of fall for the discs are compared when the tubes are at atmospheric pressure and when they are evacuated.

1C30 - Measuring g

Timed Free Fall (1C30.10) An electromagnet drops a ball from heights of 1 and 2 meters. A clock starts upon release and stops when the ball strikes a cup at the bottom.

1D10 - Displacement in Two Dimensions

1D15 - Velocity, Position, and Acceleration

Sliding Weights on Right Triangle (1D15.41) A wire frame triangle is positioned so that beads sliding down the wires traverse each side in the same time.

1D40 - Motion of the Center of Mass

1D50 - Central Forces

Ball on a String (1D50.10) A ball on string is swung around to show the basics of circular motion. Run the string through a handheld tube, start the ball spinning with all the string out, and then pull the string through the tube to decrease the radius of the ball's rotation. The ball will gain angular velocity to conserve angular momentum.

Conical Pendulum (1D50.25) String and weight pendulum swung in a circle.

Rotor (Carnival Ride Model) (1D50.30) A horizontal disc rotating at about 2 rev/s has a small section of a vertical wall at the edge. At sufficient speed, the centripetal force will keep a small object pressed against the wall without falling down.

Greek Waiter’s Tray A small circular plastic plate hangs from three strings tied symmetrically to its edge. The three strings are tied together at the top so that the plate hangs horizontally beneath them. A small glass of water is placed at the center of the plate. The plate can now be swung around in any direction, and the surface of the water in the glass will always stay parallel to the plate. The plate can also be swung overhead without spilling a drop.

Arrow Disc A wooden disc with an arrow showing one direction of rotation and an arrow along the axis showing the direction of the angular momentum vector for that spin direction.

1D52 - Deformation by Central Forces

Flattening Earth (1D52.10) A flexible hoop becomes oblate when rotated.

Rotating Rubber Wheel (1D52.61) A flat spoked rubber wheel is rotated at high speed with a motor and expands outward slightly.

1D55 - Centrifugal Escape

Circular Track with Gap (1D55.10) A ball bearing is rolled around the inside of a circular track. Students predict which path the ball will take when it reaches the opening. Uses the document camera.

Rotating Disk with Erasers (1D55.30) A horizontal rotating disc with a smooth surface. Chalk board erasers with various surfaces are placed on the disc, which is rotated slowly until the erasers slide off; how long this takes depends on rotation speed, distance from the center, and eraser surface. A weight attached to the rotation axis by a rubber band shows qualitatively how the centripetal force increases with rotation speed.

1D60 - Projectile Motion

Vertical Gun on Car (1D60.10) A vertical spring cannon is mounted to a cart running on a horizontal track. The cannon shoots a small ball vertically while the cart rolls horizontally. Since the cart travels at (nearly) constant velocity, the ball goes up and falls back into the cannon's top, staying directly above the cannon while in the air. Note: The Pasco apparatus can drift after firing. Be sure to check the aiming screws before repeating.

Drop and Shoot (1D60.20) A spring shoots one pool ball horizontally while simultaneously dropping another ball vertically. Both balls strike the floor simultaneously. Have a student volunteer catch the projected ball after the first bounce, while you catch the dropped ball.

Range Gun (1D60.40) A spring launcher shoots a wood ball at various angles and the distance traveled is marked. A large digital stopclock can be used to show times.

1E10 - Moving Reference Frames

Bulldozer on Plastic Sheet (1D or 2D) (1E10.10) One battery powered vehicle runs at a constant speed across the lecture table while a second runs across on a large sheet of plastic. Push or pull on the plastic sheet to show how velocities add or subtract. This can be done in one dimension or two; or used for frames of reference discussions.

"Frames of Reference" (1960) (1E10.20) An excellent film (black & white, 1960, approx 28 minutes) showing the apparent motion of objects with respect to various inertial and non-inertial frames of reference. Available on laserdisk or as an MPEG file from https://www.archive.org/details/frames_of_reference.

1E20 - Rotating Reference Frames

1F10 - Measuring Inertia

Inertia Balance (1F10.11) A platform is supported by two strips of spring steel, leaving it free to oscillate horizontally. Two blocks of similar appearance but different mass are placed on the platform; the lighter block oscillates at a higher frequency than the heavier block.

1F20 - Inertia of Rest

Inertia Block (Inertia Ball) (1F20.10) A heavy block is suspended between two loops of string. A slow and steady pull on the bottom loop will break the upper string, while a quick jerk will break only the lower string (due to the high inertia of the mass).

Eggs and Pizza Pan (1F20.35) Three raw eggs are propped up by cardboard cylinders which are standing on a round baking sheet. The baking sheet sits on three water filled beakers with a beaker directly under each egg. The pie sheet is knocked out by a broom (check on technique!), and the eggs drop straight down into the beakers of water.

1F30 - Inertia of Motion

1G10 - Force, Mass, and Acceleration

Heavy Cart with Spring or Spring Scale (1G10.15) A small wheeled cart is pulled along the table by a spring or spring scale with different forces to show different accelerations. The spring will give a smoother indication of a constant force (the scale bounces) but cannot give quantitative results. Weights may be added to vary the cart's mass.

Atwood's Machine (1G10.40) Two equal masses are attached to either end of a cord running over a pulley. Small additional weights can be added to one of the hanging masses to unbalance to weights and accelerate the system. A stopclock and a two meter stick can be used to show that acceleration is proportional to the unbalanced force.

1G20 - Accelerated Reference Frames

1H10 - Action and Reaction

Fan Car with Sail (1H10.20) A car with onboard fan and removeable "sail." Cart will not move at all with the sail perpendicular to the fan, but moves with the sail removed.

1H11 - Recoil

1J10 - Finding Center of Gravity

Irregular Objects (1J10.12) A piece of wood of irregular shape is hung on a metal pin from various points around its edge. Since the center of mass is directly beneath the point of support in each case, one can find it by using a plumb bob to draw vertical lines from two or more points of support - the lines intersect at the center of mass.

1J11 - Exceeding Center of Gravity

Leaning Tower of Pisa (1J11.10) A model tower leans on a slanted base and is stable until a cap is added to the top; that shifts the center of mass outside the base and the tower topples.

1J20 - Stable, Unstable, and Neutral Equilibrium

Stability of Geometric Shapes (1J20.11) A cone, cylinder, cube, and a sphere are used to discuss stability and equilibrium conditions. The sphere has neutral stability. The cone and cylinder are either in neutral, stable or unstable equilibria depending on how they rest on a surface.

Chair on a Pedestal (1J20.51) A chair with weighted legs balances on a pointed rod. Since the center of mass is below the point of support the chair is stable and may be knocked around without falling over.

Double Cone on Incline (1J20.70) Two rails fastened together at a small angle form an incline; a cylinder will roll down the incline but a double cone will roll "up" the incline because the widening of the rails allows it to lower its center of mass by moving in that direction.

1J30 - Resolution of Forces

Load on Removable Incline (1J30.10) A cart rests against a support block on an incline. A force can be applied parallel to the incline by a weight strung over a pulley, which is equal to the component of gravitational force in that direction. The support block can now be removed. Another weight is used to balance the normal force perpendicular to the incline; the incline can now also be removed. The cart will remain suspended in air.

Boom and Weight (1J30.40) A long boom is hinged at one end and supported by a cable at the other end. A large spring scale measures the force on the cable. Weights can be hung along the boom and the spring scale shows the resulting tension in the cable.

Force Board (1J30.50) Three strings are tied together to a common point, with their other ends passing over three pulleys and supporting three weights. Two different combinations of weights and string angles are available that will leave the common point in equilibrium under the three forces.

1J40 - Static Torque

Torque Bar (1J40.10) A T shaped rod with screw eyes spaced along its length. A weight is hooked to an eye and lifted off the table by twisting your wrists. The farther from your wrists the weight is, the harder it gets. Good for student participation.

Balancing Meter Stick (1J40.20) A meter stick which pivots at the center is supplied with masses which may be attached to the stick at various points to achieve different equilibria. Masses and distances are all simple 1:2:3 ratios for ease of calculation in class.

Hinge Board (1J40.21) A flat board with hooks at intervals is attached to the table by a hinge. Lift the board at different distances from the hinge with a spring scale, and observe the force required.

Torque Wheel (1J40.25) A wheel with coaxial pulleys of 5, 10, 15, and 20 cm to show static equilibrium of combinations of weights at various radii.

Bridge and Truck (1J40.40) A long board with position markings is supported at each end by a kitchen scale. A 10 lb. toy truck is rolled to different positions along the bridge while the forces at each end of the bridge are indicated by the scales.

1K10 - Dynamic Torque

Ladder Forces (1K10.20) A model ladder is positioned as though it were leaning against a wall, but is actually supported by three spring scales that provide the horizontal "wall" force and the horizontal and vertical "floor" forces needed to keep the ladder in equilibrium. A weight can be hung from various rungs of the ladder to vary the forces, which are read directly off the scales.

Large Spool with Wrapped Ribbon (Walking the Spool) (1K10.30) A large spool has a flat ribbon wrapped around its axle several times so that it will come off the bottom of the axle's shank as the spool rolls along the table. The spool will either roll clockwise, counter-clockwise, or slide without rolling, depending on the angle at which the ribbon is pulled.

Loaded Disc Rolling Uphill (1K10.50) A large disc has a lead weight hidden near one edge, so its center of mass is away from the center of the disc. If it is placed on an incline with the lead weight on the uphill side of the incline, it will roll uphill slightly because that lowers its center of mass.

1K20 - Friction

Four Surface Incline (1K20.10) A board is covered with strips of four different materials (teflon, sandpaper, bare wood, and rubber) that run down the length of the board. Identical brass blocks are placed at the end of each, and the end of the board near the blocks is slowly lifted up. As the angle increases, the blocks will slide down the strip in order of the different coefficients of friction.

Area Dependence of Friction (Plank and Weights with Spring Scale) (1K20.20) Pull a 2x12 plank along a level table at constant speed with a spring scale. Friction is approximately independent of which face the plank is sliding on (narrow or wide) and the plank's velocity. Add masses to increase frictional force.

Incline with Sliding Blocks (1K20.35) Blocks with different surfaces are placed on an incline, which is slowly raised until the block just begins to slide down. The tangent of the angle at that point equals the coefficient of static friction between the inclined board and the sliding block.

1K30 - Pressure

1L10 - Universal Gravitational Constant

Cavendish Balance Model (1L10.20) A large scale open model of the Cavendish balance.

Cavendish Balance Experiment and Video (1L10.30) Cavendish balance experiment which can measure the value of G to within 10% or less. Note: This experiment takes about 90 minutes to perform so most instructors use the video instead.

1L20 - Orbits

Conic Sections (1L20.40) A dissectable cone is cut several ways to give a circle, ellipse, parabola, and hyperbola.

Ellipse Drawing Board (1L20.51) An acrylic board with two adjustable pins and loops of string. Works well with the document camera.

1M10 - Work

Pile Driver with Nails (1M10.20) Five nails are just barely driven into a piece of wood. Masses slide down a rod and strike the heads of the nails one by one, driving them into the wood. The penetration depths of the nails are compared as an indicator of the energy released in four different configurations (two different heights and two masses) versus the control nail. Note: See also Pile Driver with Foam (1N10.30).

1M20 - Simple Machines

4:1 Ratio Pulleys Two pulleys with a 4:1 diameter ratio are bound together on a common axle. A weight on the large pulley is balanced by four times as much weight on the smaller.

1M40 - Conservation of Energy

Galileo's Pendulum (1M40.15) A pendulum swings in front of a white board with horizontal marks. The string strikes a stationary peg, which stops the top part of the string and shortens the pendulum, but the bob always rises close to the initial height.

Loop the Loop (1M40.20) A ball rolls down a straight section into a vertical circular loop and then into a uphill incline.

Energy Well Track (1M40.25) A ball rolls down an incline and up a shorter hill on the other side. If the ball's initial height is below a given mark, the ball will not have enough energy to roll up and over the hill, but will instead roll back and forth between the two inclines.

Triple Angle Track (1M40.33) Three inclined tracks each have the same downward slope, but different uphill angles on the other side. A ball rolled down each track in turn rolls up the other side to the same height in each case, despite the different slopes.

Ballistic Pendulum (1M40.41) A commercial ballistic pendulum apparatus that fires a ball bearing into a swinging arm catch mechanism.

Spring Jumper (1M40.67) A small jumping toy which shows that a spring may contain enough energy to launch itself into the air.

High Bounce Paradox (1M40.91) A raquetball that’s been cut in half. Invert the curve of the ball with your hand. When dropped, the ball will pop back upon colliding with the floor, releasing the stored energy you put in and making it bounce higher than the release height.

1M50 - Mechanical Power

Prony Brake (1M50.10) A student cranks on the handle for one minute against a constant frictional force. Knowing the drum circumference, the number of turns (and thus distance traveled), the force, and the time, horsepower can be calculated (about 0.25 hp max).

1N10 - Impulse and Thrust

Pile Driver with Foam (1N10.30) A pile driver drops a mass onto a plastic strip and cracks it, but not if a piece of foam is placed on the board. Same impulse, different force and time. Note: See also Pile Driver with Nails (1M10.20).

1N20 - Conservation of Linear Momentum

Reaction Carts Two rolling carts, one with a spring-loaded plunger, are tied together with a string. The string is burned, and the two carts are pushed apart by the spring and roll away with equal and opposite momentum. A large weight can be added to one cart to increase mass.

See-Saw Center of Mass (1N20.10) The Reaction Carts are balanced on a long see-saw board so that their center of mass is directly above the fulcrum. The board is horizontal and stable. When the string between the carts is burned, they spring apart with equal and opposite momenta. The center of mass remains above the fulcrum so the board remains balanced (until one cart strikes the end of the board). Most dramatic with different mass carts.

Radio Controlled Car on Rolling Board (Dog on Boat) (1N20.15) A radio controlled car sits on top of a short board that is mounted on wheels. Moving the car forward moves the board backward, and vice versa.

1N22 - Rockets

Water Rocket (1N22.20) A toy plastic water rocket uses pressurized air as a driving force. The amount of lift varies greatly with the selection of the exhaust: air exhaust will barely move the rocket (low mass transfer), but water exhaust can easily send the rocket to the ceiling.

CO2 Rotator (1N22.33) A CO2 cartridge is inserted in a cylinder at the end of a rotation arm. When the end of the cartridge is punctured, the escaping CO2 spins the arm in a circle.

1N30 - Collisions in One Dimension

Newton’s Cradle (1N30.10) 5 stainless steel balls demonstrate conservation of momentum and energy.

Eleven Pool Balls (1N30.15) Eleven pool balls are suspended linearly. One or more balls can be separated together and released to collide with the remaining balls, and the same number of balls fly off other end. This is similar to the Newton’s Cradle above, but doesn’t work quite as well because the pool balls have a lower coefficient of restitution than the stainless steel balls.

Collision Balls (Various Masses) (1N30.20) Two balls are suspended side by side so that one may be swung out and released to strike the other. Available in mass ratios of 1:1, 1:3, and 1:80. Velcro may be used on the 1:1 balls to produce inelastic collisions.

Double Ball Drop (1N30.60) A tennis ball and basketball are dropped with one on top of the other.

Astro-Blaster Toy Five rubber balls of diminishing size are threaded on a common rod through holes in their middles. The balls are free to slide on the rod, but only the top (smallest) ball is free to come off the rod. If the stack of balls is dropped on the floor, the ratio of the ball masses is such that most of the momentum and energy of the four lower balls is transferred into the top ball during the collision with the floor. The top ball flies off the stick to a much greater height than the drop height.

1N40 - Collisions in Two Dimensions

1Q10 - Moment of Inertia

1Q20 - Rotational Energy

Angular Acceleration Machine (1Q20.10) A flat bar free to rotate about its center is accelerated by the torque provided by a string-wrapped disc and hanging weight. Two weights attached to the bar may be removed, placed close to the center of the bar or at the ends of the bar for three different moments of inertia. Accelerating weights may be varied, and can be hung on either a 5 cm or 10 cm disc to change torque - observe varying angular accelerations.

Spool Wheel on Incline (1Q20.30) A large spool with a small hub rolls down an incline on the hub. When it nears the bottom of the incline the large outer discs touch down and the wheel rolls on the discs instead of the hub. Since points on the edge of the outer discs have a much greater translational velocity than points on the hub, the wheel as a whole gains translational velocity. To compensate, it loses rotational velocity.

Bicycle Wheel on Incline with Lockable Hub (1Q20.35) A bicycle wheel with a center hub that can be left free to rotate or locked to the wheel rolls down an incline on the hub. When the hub is locked, a large amount of energy must go into the angular momentum of the wheel as it rolls, so the translational velocity is much lower than with the hub free.

Falling Chimney (Faster Than g) (1Q20.50) Two boards are fixed together by a hinge at one end so as to allow them to fold together. One board is flat on the table and the other board is propped up by a stick, with a ball balanced on a golf tee attached to the end of the board. When the stick is pulled away and the board is released to free fall, there is a torque about the hinge and rotates as it falls. The rotation causes the end below the ball to accelerate faster than the ball and the ball falls into the cup.

1Q30 - Transfer of Angular Momentum

Satellite Derotator (1Q30.25) Two heavy weights on cables are released from a vertically spinning disc to stop the system by conservation of angular momentum.

1Q40 - Conservation of Angular Momentum

Rotating Stool and Weights (1Q40.10) Sit on a rotating stool holding a dumbell in each hand; pulling the dumbells inward will increase your angular velocity, letting them out will decrease it.

Watt's Governor (1Q40.23) A small model of a Watt governor is spun to increase angular velocity.

Rotating Stool and Bicycle Wheel (1Q40.30) Sit on a rotating stool holding a spinning bicycle wheel in your hands. Tip the wheel and the stool will rotate to conserve the angular momentum of the system.

Wheel and Brake (1Q40.45) A horizontal bicycle wheel is contained in a frame that is free to rotate in the same plane as the wheel. A braking device mounted to the frame is held open by a string; burn the string and the brake clamps down on the wheel, transferring angular momentum from the wheel to the frame and making both rotate together at a lower velocity.

Marbles and Funnel (1Q40.70) Marbles roll into a large glass funnel. The marbles spiral downward and rapidly increase their rate of rotation, due to conservation of angular momentum. Finally they reach an equilibrium level where they revolve in a nearly horizontal plane, gradually dropping lower as friction slows them down.

Air Rotator with Deflectors (1Q40.82) A rotating bar has tangential air jets at the ends of the arms and deflectors which may be swung into the air streams. If the deflectors are out of the air streams, the device will rotate like a garden sprinkler. If the deflectors are in, and air velocity is low, no rotation is observed because the reaction force of the air leaving the jet is balanced by the force of the air striking the deflectors.

1Q50 - Gyroscopes

Gyroscopes Choose from various gyroscopes, from simple toys to high quality demonstration models. Select this entry for general gyroscope info and references.

Handheld Gyroscope A gimbal mounted gyroscope will maintain its axis of rotation when it is moved around the room.

Gyroscope with Adjustable Weight (1Q50.20) A small gyroscope with a movable counterweight on its axis for precession.

Bicycle Wheel on Gimbals (1Q50.22) A heavy bicycle wheel in two-axis gimbals.

Bicycle Wheel Precession (1Q50.23) A bicycle wheel with handles which may be spun up with a string wrapped around the hub. It can then be suspended by a rope tied to one handle to show precession. Will also precess when stood on its end like a top.

Double Bicycle Wheel (1Q50.25) Two bicycle wheels on a common axis. If they are rotating in the same direction they will precess, but if they are rotating in opposite directions their net angular momentum is zero and they simply fall over.

Motorized Gyroscope (Precession and Nutation) (1Q50.30) A motorized gyroscope with a heavy flywheel on gimbals. Weights may be hung from the end of the bearing arm to produce precession and nutation. The flywheel takes over a minute to come up to full speed, and if a weight is hung on the arm when the spin is still slow, precession will initially be rapid but will slow down as the flywheel speeds up.

1Q60 - Rotational Stability

Tippy Top (1Q60.30) A top that flips upside down and spins on its handle.

1R10 - Hooke's Law

1R20 - Tensile and Compressive Stress

High and Low Elastic Limits (1R20.11) A plastic slinky spring may be stretched a long way and will still return to its original length. A copper coil stretched even a short distance won't return to its original length.

Young's Modulus (1R20.15) A long wire mounted in a vertical stand has a weight hanger on one end and a small platform partway down on which a pivoting mirror sits. Add weights to the weight hanger and the wire stretches, pivoting the mirror and deflecting a laser beam. The spot on the wall moves farther with each added weight.

1R30 - Shear Stress

1R40 - Coefficient of Restitution

Happy and Sad Balls (1R40.30) Two rubber balls that look similar but have different elasticities are dropped on a table. One bounces, one doesn't.

1R50 - Crystal Structure