Physics Teachers' Inventions Fair proceedings

About paper

Czech original

Polák Z.

Is the CD a good read-write medium? Well, you can write on it, but I broke three typewriters trying to use it. If you want to write something on it, only a felt-tip pen will work; it won’t fit a lot of handwritten notes, though. Nevertheless, it is a piece of beautiful material. It openly invites you to a closer examination. CDs are everywhere, everyone has seen them. What do we know about them? Literature and the Internet give us some parameters. But you cannot believe everything on the web; it is better to measure whatever you can.

The manufacturer lists these dimensions:

Disk diameter: 12 cm

Hole diameter: 15 mm

Weight: 18 g

Here are some basic dimensions of 15 randomly selected CD disks:

D – outer diameter

d – hole diameter

h₁ – smallest thickness measured

h₂ – largest thickness measured

m – weight of disk in grams

ρ – density of disk in kg/m²

The hole and disk diameter were measured three times each and no measurable deviations were found. The disk is circular enough. The thickness was measured three times on the edge and three times approximately 3 cm away from the edge. Highest and lowest thicknesses were measured. Usually, the edge had a higher thickness.

From these values can be concluded, that the data given by the manufacturer are correct. What is different, however, is the weight – the CDs are lighter. It doesn’t matter whether the CD is pressed, CD-R or CD-RW, they all have the same density of 1190 kg/m³.

After getting familiar with the disk many ideas for experiments will occur to us.

Determining the density

a) We determine the size and weight, then calculate the density (see table above). A good idea for experimental work with students.

b) We hang the CD from a dynamometer with the highest value of 0.2 N, measure the gravity in air F₁and in water F₂. The density \( \rho = \rho_v \frac{F_1}{F_1 - F_2} \), where ρv is the density of water.

c) Floating in liquid. This is especially impressive. We prepare two solutions with densities of around 1175 kg/m³ and 1205 kg/m³. We cut the CD into pieces, place it in the two solutions, get rid of any bubbles that might form on them and describe their behaviour. In the lower density solution the CD will fall to the bottom, in the other it will float up to the surface. We let students mix the two solutions together to form one in which the CD will float. They find the balance to be surprisingly unstable and that to mix the right solution is not simple. Lastly, we determine the density of the resulting solution using a densimeter or a Westphal balance.

Any safe solution will do. In my opinion, glycerine with maximum density of 1260 kg/m³ or simple sugar works best. The density of saccharose-saturated solution is approximately 1350 kg/m³. To get the aforementioned densities (kg/m³ and 1205 kg/m³) mix 207 or 230 g of sugar and fill to 500 g with distilled water. The densities are purely orientational, a lot depends on temperature!

Determining π

We mark a point on the edge of the CD with a thin felt-tip pen. We prepare a long-enough strip of paper. We draw a straight line along the whole length of the strip of paper and draw the start of the line segment a small distance from the edge. We put the CD on our finger like a ring, place the CD mark on the start of the line segment and roll. When the mark on the CD touches the paper again, we mark the end of the line segment. We measure the length and divide it by the diameter of the CD. We can use several rotations. Then, we can create a simple statistic from the students’ results.

Determining the moment of inertia

The moment of inertia is a physical quantity, which is tangentially touched on in the first year of secondary school education. However, it is something we need to understand the behaviour of a rotating object. According to the students’ skills we can choose a variety of ways.

a) Calculate from the measured size and weight, create an equation: \( J= \frac{m}{8} (D^2-d^2) \).

b) From the acceleration of the CD rolling on a sloped surface. We connect two CDs with a short tube and place them on a slope with a very small incline. If we mark the height h of the inclined plane, length l and the time t of the CD rolling down the plane, then the moment of inertia can be determined from the equation \( J=\frac{mD^2}{6}\left( \frac{ght^2}{2l^2} - 1 \right) \), where m is half the weight of the pair of CDs.

c) From the oscillation duration of the CD. We drill a series of holes 5 mm in diameter whose distance from the centre is 10 to 55 mm. We prepare a simple stand with a thin axis of rotation. A wooden stick with a metal needle or a small tack works best. We place the CD on the axis and let it swing. We measure the relation between the time of 1 oscillation and the distance of the hole from the centre of the CD.

We derive a formula and process the large amount of measured data (preferably in Excel): \( J = mx \left( \frac{gT^2}{4\pi^2} - x \right) \), where x is the distance of the axis of rotation from the centre of the CD. The relation of the position of the axis of rotation and the duration of one oscillation is very interesting in itself and it is suitable for examination.

There are, of course, more ways which can be used to determine the moment of inertia. The average figure of a CD is 3×10^-5 kg×m² doesn’t tell us a lot. It is more suitable to point to the energy of the CD while the CD drive works and the change of energy during the starting and stopping of the disk, e.g. while reading starts on the inner track with 12x speed the disk rotates approximately at 108 RPS and with an energy of 7 J, which is enough to fling it 45 meters vertically into the air.

A CD flywheel

a) We cut a thick felt-tip pen in two pieces, the one with the tip approximately 4 inches long. We take out the felt tip and drill the hole out to a diameter of 5 – 6 mm. We sharpen the tip and push it through the hole. A small wooden dowel is suitable.

b) A ball-bearing flywheel. We need a hard disk drive bearing, a thick felt-tip pen cap and a small plastic stick. A piece from a suitable leftover ballpoint pen can be used as well. From the pen cap cut a 2 cm tube. Then we screw the bearings on our stick, push it inside the cap tube and on the top we push a couple of CDs. Then all we need to do is spool a string close to the CDs and start it by pulling quickly. We can demonstrate simply the effectsof the moment of force of a gyroscope.

Maxwell’s pendulum

We place several (2 - 10) CDs onto a plastic pipe. We then drill a small hole in the pipe around 5 mm from the edge and pull two 0.5 meter long strings through. The strings are then hung onto a horizontal suspension and wound up around the CD pipe. Then just let the disk go. We can make several pendulums with different middle pipe diameters and compare the acceleration of the individual pendulums.

Magnet momentum wheel

We use a ball bearing flywheel and put only one CD with a coordinate grid. Afterwards, we place magnets on suitable spots on the grid as weight and show different options of balancing the momentums of force. This has an advantage over a lever which is the ability to place the weight in points, the connecting line of which does not go through the centre of rotation.

CD rigidity and elastic energy of a CD

We prepare several hardboard boards. Place a CD with parallel lines drawn on, about a centimetre apart. The CD is then gripped between the two boards so that two boards are above and two below the CD. The whole object is placed on a table and the CD is bent to the surface of the table. After each push the CD is inserted deeper between the boards to the next line. The force needed is greater, although the deviation is still the same. The rigidity of the elastic framework changes. Then the CD is pushed halfway between the boards. On the end we place a rubber on the end of the CD and shoot it upwards. We let the students describe how the height of the shot changes if the CD is 1, 2, 3 or 4 boards away from the table. We show how the maximum height of the shot rises faster than the number of boards. The energy of elasticity is not proportional to the deviation itself, but instead to the square of the deviation. Then we discuss the work done, conversion of energy and its transfer between objects.

Floating CD and a compass needle

In our previous experiment with densities we concluded that a CD will sink in water. However, if we place it on a calm water surface, it floats. The surface tension stops it from sinking, it can even sustain more weight, e.g. two magnets from a CD ROM reading head. And boom, our boat just turned into a compass needle. It will turn on the surface of the water so that the two magnets are parallel to Earth’s magnetic field.

Needle bearing

We glue a board with a push stud in the middle into the middle of the CD. Then we place the object on the tip of a needle on a stand and spin it. The students will be very surprised by how long the disk actually spins.

CD capacitor

We use double-sided tape to affix aluminium foil to a CD. With a hot-glue gun, we glue a piece of hard PVC pipe with a socket, after which we connect the aluminium foil to the socket using a wire. We prepare a second CD in the same way. Then, we drill two small holes, through which we pull a thin copper line as a contact. Another CD (or more suitably an overhead projector film) will serve as a dielectric. With a connected capacitance meter we can demonstrate the change of capacity with different distance of the disks and all the experiments conducted with a parallel-plate capacitor.

CD as an electric current conductor

All types of CDs, whether pressed or burned have a thin layer of metal with a high reflectivity, protected from one side with the plastic of the medium and from the other with a layer of lacquer and paint. It is basically a sandwich of organic insulants filled with metal. According to the type of the CD it can be either aluminium, gold, or silver. We take an ohmmeter with the wires ended in crocodile clips. If we touch only the surface, the resistance is immeasurable. However, if we bite into the layer of plastic and lacquer, the teeth touch the metal layer and the resistance drops to ohms.

The existence of a conductive layer can be also proven in other ways. Have you ever put a metal-rimmed cup in a microwave oven? And did you see what it does? You haven’t? And you don’t want to ruin you grandma’s old tea set? Well then, if you have enough CDs and aren’t afraid about your microwave oven, you can perform this very interesting experiment. You place a CD on a glass and start it for around 2 seconds. Very strong eddy currents are induced in the thin conductive layer of the disk. The metal layer heats up and is disintegrated in many spots on the disk. The remaining metal plates create interesting patterns. I don’t know how much your microwave liked it and I’m very much interested in what the manufacturer would say.

Wave optics on a CD

The CD is a very interesting optical medium. The published experiments most often talk about interference on a reflecting diffraction grating. This way, we can, for example, create a rainbow.

For this experiment we need a suitably powerful light source. We can either use direct sunlight or a slide projector. In the first case we darken the classroom except for one window. We place the CD in a stand or simply hold it in our hand, on the edge of the light beam coming through the window so that we create a light reflection on the wall with the direct light beam. Around it, we can see two concentric rainbows. This experiment is quick, simple, but the rainbows are hard to distinguish.

It is better to use the diffraction of a slide projector light. We place the slide projector on a desk around 50 or 60 cm from a white large shade (a white wall, or a screen around 2 × 2 metres). We place an empty slide into the slide projector and tilt it so that the light beam goes into the classroom, upward and under an angle. Then we place a CD in a stand in a vertical position. If we can’t create a special holder, a magnet can hold the CD to a metal pipe. On the wall, two concentric rainbows will form. They are first order diffraction peaks. This can be proven by covering one half of the CD.

The CD doesn’t necessarily need to serve as a diffraction grating. The maker of the CD prints a guiding groove into the disk, similar to a gramophone record. If, however you get a plastic disk from the CD without the metal layer, you can make several interesting experiments as you would with a diffractive grating. The easiest way is to buy such a CD from distributors and buyers. CDs intended for burning of data are sold in packs of fifty and on the ends of the package are protective disks, which are basically just like CDs, only without the metal layer.

Let’s do another interesting experiment. We observe how the intensity of reflected laser beam depends on the orientation of the laser and the angle of incidence on the plastic surface of the CD. It is better to do the experiment first on the CD box and then on the disk itself. When the light is reflected off the CD, we can observe the zero order peak together with several higher order interference peaks, which only disturb. We show that the light of a laser is partially polarized.

If we measure the angle at which the lowest amount of polarized laser light is reflected, we can determine the refractive index of a CD from the formula of Brewster’s angle n = tgα.

CD drive experiments

What is inside a CD-ROM?

A CD-ROM drive is a physicist’s treasure island. There is a series of interesting things hidden inside this box, weighing just under a kilogram. What is inside a wreckage of a CD-ROM? Take the following list of components only as an orientational one, as different drives can vary a lot from one another.

1) A dismountable sheet metal casing.

2) A motor with a magnetic CD holder, all in a friendly-looking frame. Ideal for the spinning of just about anything. If you are lucky, it is a 5 V DC motor. The two outlets on the underside are a tell-tale sign that it is what you are looking for. Otherwise, you get a three-phase synchronous motor and to make it spin you need complicated electronics. The latter one usually has 8 or more wires coming out of it. In such a case, however, you get a strong magnet from the CD holder and three Hall linear sensors (if you gut the motor).

3) Two 5 V DC motors.

4) One or two plastic lenses from the CD-ROM optical system. Their diameter is 3-4 mm. The focus is from 3 to 15 mm, depending on whether the focusing system has one or more lenses.

5) Reflectors or prisms with a thin surface interference layer.

6) Wonderful tiny neodymium magnets from the focusing system of the CD-ROM optics. Millimetres in size, weigh from 0.2 g to 1 g.

Coupled CD drives

We take the CD drive with the CD spinner out of two CD drives. Then, we wire them together with two parallel wires. If we turn one of the disk drives, we turn the motor inside, this creates electric current. The current spins the motor in the other drive and it moves. A classic example of work-energy transfer.

We can connect the tracking drives in the same way, or combine both types of the drives.

Small current detection

The motor of a CD drive turns even at a voltage of only 0.6 V and a current of 20 mA! It is therefore suitable to demonstrate the existence of voltage on photocells, galvanic cells or during electromagnetic induction.

Mixing colours on a rotating disk

We place the magnetic CD holder with the frame and the motor on a wooden board. From paper, we cut disks the same size as the CD and make a colourful surface from them; this we clip with a magnetic holder to the motor, together with the CD. We connect a 3-9 V voltage source. The motor will survive the short-term overload.

Motor–generator from CD motors

We place two motors on a board with a shaft connecting the two. One serves as a motor, the other as a generator. We connect a small light-bulb to the generator (it should have an energy input as low as possible).

CD stroboscope

Cut two symmetric segments from the CD. We fix them to the machine for mixing colours and we can observe a periodical process directly through the rotating CD; or we can let light pass through the CD and illuminate some process this way.

CD fan

We cut the CD 4 cm into the middle in 16 places. In hot air we bend the individual blades of the fan and let them harden in cold air. A hot air gun or a burner can create hot air, the cold air is created by a fan.

Kepler telescope

We glue the lens from the laser focusing system in the middle of a photographic film box. Inside a champagne cork we drill a hole and place the lens of an old camera. We push the cork inside the hole and focus by moving the cork. The image is turned upside down.

Magnet fall

It is very impressive to let neodymium magnets from the reading head of a CD-ROM fall through a copper pipe. We need several such magnets. By connecting them together, we get a small cube of millimetres in size. From a heating technician we get a copper pipe with the inner diameter just about 1 mm larger than the diagonal of the magnet cube. Then we prepare a similar magnet from a ferritic magnet.

Through a vertical pipe, we first drop a metal cube. The fall is very fast. Then we let the ferritic magnet fall through. Now, the fall is slower. Lastly, we let the neodymium magnet fall through the pipe. The 70 cm pipe fall takes more than 15 seconds!

Some links, where you can find something about CDs and more.

www.stud.fee.vutbr.cz/~xnedve01

www.ped.muni.cz/wphy/NEDVED/cd1.htm

www.cdr.cz

www.cdr.cz/cojeco/vyroba_cdr.html

www.cdr.cz/cojeco/CDR.htm

www.cdr.cz/cojeco/rychlost_otaceni.html

www.cdr.cz/cojeco/overburning.html

www.cdr.cz/cojeco/CDRW.htm

www.cdr.cz/cojeco/barviva.html

www.diskus.cz/cz/tipy/tipy.htm

www.diskus.cz/cz/tipy/porovnani.htm

www.stereovideo.cz/9912/top.html

lide.pruvodce.cz/cherry/Cdrom.htm

www.pvtnet.cz/www/gramofonove/Cz/TC/TP_-_CD_Potisk.htm

www.pvtnet.cz/www/gramofonove/Cz/TC/TP_-_GD.htm

http://fyzika.gymnachod.cz