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I set a coordinate system on the cone apex, with $+\hat{y}$ pointing up and $+\hat{x}$ pointing radially out at an azimouth (location) angle $\theta=0$. The position of the ball is defined by the distance from the apex up the slope to the ball $r$ and the longitude around the cone $\theta$ $$\vec{p} = {\rm Rot}(\hat{y}, \theta) \begin{pmatrix} r \sin \psi ...


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To understand it in the easiest way either look at it as frequency... What you are describing is the frequency $f$. The frequency is an amount of turns or revolutions or periods or something else that happen every second. Your frequency here is $n$ turns per second. Then you have this formula to find angular frequency: $\omega=2 \pi f$ Or as a number of ...


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If you look at this video which claims to be a "world record spin", they claim they measured the speed (308 rpm!) with a "Sport Tach" - see for example review at http://figureskating.about.com/od/accessories/gr/sporttach.htm . Tried to follow links to their website - it seems their domain is for sale so I suspect they have gone out of business. When you ...


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If you don't want to do video, you could try with a smartphone. There are apps which can record the sensor measurements, including the accelerometer and the gyroscope. I have no idea how noisy the data will be for a skater, but if the device is firmly attached to her body close to her center of mass, it may deliver useful results. From there the sky is the ...


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In this link you can find a video analyzer tool. This tool works well with videos taken even on a smartphone, and is free and made for educational purposes. https://www.cabrillo.edu/~dbrown/tracker/ Have her hold a distinct red kerchief or ball in one hand. This way the tracker can easily track her spinning. You can get frequency as well as number of ...


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I don't want to give away the answer immediately, since it's homework. Try to visualize one huge big wheel and one very small wheel. Try to imagine what would happen if at each instant the tangential velocity is not the same.



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