# Practical setup to measure angular velocity

I have got a spinning top from a Canadian manufacturer, and I am deeply amazed by how neatly it spins.

My interest in physics has led me to try to find out at what top speed I can spin the top and how that compares to other tops made from other materials and other shapes.

I have glued a little sticker to it and recorded it with my phone's camera but the frame rate is far too slow to be able to count the number of rotations over time.

I don't have access to specialized equipment but I can measure or approximate the volume, mass, density, temperature and probably also the moment of inertia. How do I measure the angular speed of the top?

• Technically, the top speed is achieved at the very beginning of the spinning; the spinning top's velocity then obviously decreases due to friction. So what you're going to measure is more of an average speed during a period of time that is "representative" of the top's rotational velocity without too much friction. The question is then, how do you determine such a period of time? – Demosthene Mar 8 '15 at 11:22
• Another idea would be to attach a string and to find the number of rotations in a certain time. The increased radius of the 'coil' might somewhat compensate the friction and slower angular speed. – ahemmetter Mar 8 '15 at 11:41
• Yes, the top speed is hard to measure, but the average speed at the beginning of the spinning is what I was asking about – ahemmetter Mar 8 '15 at 11:42
• You can buy relatively low cost optical tachometers that work either with a reflective sticker or, in many cases, just enough optical variation per rotation. With some work you could make this $5 module work or you can buy complete ones like these from about$12 – Russell McMahon Mar 8 '15 at 11:57
• The lesson here is: Don't take the advice of random users without checking for official guidance. Ideally, you would have deleted the question on the original site before it received an answer, or enlisted the help of a moderator to migrate the question here. Now we have two of the same question, answered, on two sites, which is not ideal but hardly the end of the world. Keep it in mind for next time and the moderators will handle it from here. – Air Mar 8 '15 at 15:59

There are several ways.

The most direct is to paint half of the top white and the other black, then point something with a light sensor at it. AC amplify the output a little, then determine the frequency. This could be with a deliberate frequency counter, a scope that displays frequency directly, or a microcontroller you program to find the period and ultimately show you the frequency.

A off the shelf method is called a Strobe Tach. This isn't a direct frequency measurment, but can work pretty well nonetheless. It is a strobe that flashes at a calibrated rate that you can adjust. You adjust the stobe flashing to appear to "freeze" the spinning top, then look at what frequency the strobe is set to.

Yet another way it to put the top on something coupled to a microphone. There will inevitably be some imbalance, which will cause vibration at the rotation frequency. This can be amplified and the frequency determined like the light signal in the first suggestion.

If you can magnetize the spinning thing, then you can use a magnetic pickup to get a similar signal than the light sensor or microphone would produce.

Probably the easiest practical method to measure the frequency of a spinning top with everyday equipment is to analyze the sound created by the motion and look for the characteristic frequency. This can be done with a spectrum analyzer app that should be available for free for most smartphones.

Place the spinning top close to the microphone of the phone and record the sound with the spectrum analyzer app. You should see several peaks in the frequency spectrum that slowly move towards lower frequencies while the top is spinning down. The lowest one should be the rotation frequency, and the other ones are harmonics at integer multiples.

In order to get a clear signal you need the top to make a measurable sound. Placing it on top of a hollow resonator might help. Also, if the top spins on a surface that has some roughness this will significantly enhance the sound, but it might disturb what you want to measure.

The picture shows a quick test I just did. I used an iPhone app called "Spectrum Analyzer" which has a nice spectrogram mode. As you can see (though the scale is admittedly hard to read) my top created a sound whose lowest frequency component started out at a bit over 100 Hz. So the angular velocity was roughly 600 rad/s.

• +1 It's funny that this is such a simple method, but it wouldn't have been accessible to most people 5 years ago. – Chris Mueller Mar 9 '15 at 12:27

You can use the wagon wheel or stroboscopic effect and count how many times the perceived rotation reversed direction until it is stopped.

This lets you get the RPM without a super slow motion camera.

I would imagine a nice crude formula might be of help $T_p = 4\pi^2 I / mgrT_s$. So if the spin speed is too fast for you, the precession speed will be inversely proportional and very slow. Here you can see the effect of the material through its mass, but you also have to approximate the moment of inertia, as well as the perpendicular distance between the spin axis and the precession axis

• Is r the distance between the fixed point (on the surface) and the center of mass? Also, I am bot quite sure what the perpendicular distance you wrote is. Don't those axes intersect in the fixed point? – ahemmetter Mar 8 '15 at 10:29

The answer could be to get hold of a high-speed LED stroboscopic light. How easy/expensive this will be depends on the angular speed you are dealing with. There are even some phone apps which will go to moderate speeds.

You tune the speed of the stroboscope to make the mark on your spinning top appear stationary. But this will be difficult because the speed will not be constant.