In the INSTRUCTABLE "Solar Panel as a Shadow Tracker", it was presented an experimental method to determine the speed of an object from the projection of its shadow on a solar panel. Is it possible to apply some variant of this method to study rotating objects? Yes, it is possible. Next, a simple experimental apparatus will be presented that will make it possible to measure the period and frequency of rotation of an object. This experimental apparatus can be used during the study of the subject " Physics:Classical Mechanics ", in particular during the study of the topic "Rotation of rigid objects". It is potentially useful with undergraduate and graduate students, during experimental demonstrations or laboratory classes.

Step 1: Some Theoretical Notes

When a solid object rotates around an axis, its parts describe circumferences concentric to that axis. The time it takes for one of these parties to complete the circumference is called the rotation period. Period and frequency are reciprocal magnitudes. In the International System of Units the period is given in seconds (s) and the frequency in Hertz (Hz). Some instruments to measure the frequency of rotation give the values in Revolutions per Minute (rpm). To convert from Hz to rpm, simply multiply the value by 60 and you will get the rpm.

Step 2: Materials and Instruments

• Small solar panel (100mm * 28mm)

• LED Flashlight

• Reflective adhesive tape

• Black electrical tape

• Electric cable

• Cable ties

• Hot silicone gun

• Soldering iron and tin

• Three pieces of wood (45mm * 20mm * 10mm)

• Digital oscilloscope with its probe

• Rotating object to which you want to measure its rotation frequency

Step 3: Operating Principle

When light strikes an object, one part is absorbed and another reflected. Depending on the characteristics of the surface and the color of the object, that reflected light can be more or less intense. If the characteristics of a part of the surface are changed arbitrarily, let´s say by painting it or by sticking it to a silver or black adhesive tape, we could intentionally cause a change in the intensity of the light reflected in that area. Here we would not be doing a "SHADOW TRACKING" but we would be causing a change in the characteristics of the reflected lighting. If an object when rotating is illuminated by a light source and a solar panel is properly placed, so that a portion of the reflected light falls on it, a voltage must appear at its terminals. This voltage has a direct relationship with the light intensity it receives. If we change the surface, the intensity of the reflected light changes and with it the voltage of the panel. This panel could be connected to an oscilloscope and identify variations in voltage with respect to time. If we can identify a coherent and repetitive change in the curve, measuring the time it takes to repeat itself, we would determine the rotation period and with it, the frequency of rotation indirectly if we calculate it. Some oscilloscopes are capable of automatically calculating these values, but from the point of view of teaching, it is productive for students to calculate it. To simplify this experimental activity we could initially use objects that rotate at constant rpm and preferably symmetrical with respect to its axis of rotation.

Summarizing:

1. An object that rotates continuously reflects the light that falls on it.

2. The intensity of the light reflected by the rotating object depends on the color and the characteristics of its surface.

3. The voltage that appears on the solar panel depends on the intensity of the reflected light.

4. If the characteristics of a part of the surface are intentionally changed, the luminous intensity of the light reflected in that part will also change and with it the voltage in the solar panel.

5. The period of the object during rotation can be determined by measuring the time elapsed between two points with identical values of voltage and behavior with the help of an oscilloscope.

Step 4: Design, Construction and Execution of the Experiment

1. Solder two electrical conductors to the solar panel.
2. Cover the electrical contacts on the panel with hot silicone to avoid short circuits.

3. Build the wooden support by joining with hot silicone or another glue the three pieces of wood as seen in the image.

4. Stick the solar panel to the wooden support with hot silicone as shown in the picture.

5. Stick the lantern to the wooden support as shown in the picture and secure it with plastic ties.

6. Secure the electrical conductors of the panel with another flange to the wooden support.

7. Paste on the object you want to study a band of black tape and then a silver band as seen in the image.

8. Start the rotation of the object you want to study.

9. Connect the oscilloscope probe correctly to the solar panel conductors.

10. Set up your oscilloscope correctly. In my case the voltage divisions were 500mv and the time divisions 25ms (it will depend on the rotation speed of the object).

11. Place the experimental apparatus that you just assembled in a position where the light rays are reflected on the surface that rotates and hit the solar panel (help yourself from what you see in the oscilloscope to obtain a curve with more pronounced changes).

12. Keep the experimental apparatus fixed in the proper position for a few seconds to see if the results of the curve remain constant.

13. Stop the oscilloscope and analyze the curve to determine which positions correspond to the black tape and which to the silver tape. In my case, since the electric motor that I studied was golden, the changes caused by the tape became more noticeable.

14. Using the oscilloscope cursors, measure the elapsed time between the points with phase equality, first for the tape and then for the silver ribbon and compare them (they must be the same).

15. If your oscilloscope does not automatically calculate the inverse of the period (frequency), do so. You can multiply the previous value by 60 and thus get the rpm.

16. If you have the value kv or revolutions per volt (in the case that it is a motor that offers these characteristics) multiply the value kv by the input voltage, compare the result with the one obtained by you during the experiment and arrive at conclusions.

Step 5: Some Final Notes and Recommendations

It is convenient to initially check the calibration status of your oscilloscope to obtain reliable results (use the calibration signal offered by the oscilloscope, which is generally 1khz).
Adjust your oscilloscope probe correctly. You should see rectangular pulses not deformed if you use the signal generated by the oscilloscope itself (see image).
Investigate the electric response time with the manufacturer of your solar panel (datasheet). In my case it was much lower than the period of rotation of the electric motor that I studied, so I did not consider its influence on the measurements I made.
Compare the results obtained by this method with those obtained by a commercial instrument and consider advantages and disadvantages of both.

As always I will be attentive to your suggestions, comments and questions. Good luck and keep up with my upcoming projects!