How fast can you fidget?

A wierd blobby fidget spinner with too many arms. Have you ever wondered how fast your fidget spinner spins? If you want to find out, you’ll have to do some maths!

Safety: Be careful spinning your fidget spinner near the glass of your scanner or photocopier. Don’t hit the glass, as it can break.

You will need

Fidget spinner
Computer with a flatbed scanner and printer, or a photocopier
Ruler
Timer
Paper
Pen
Calculator (optional)

Strange pictures

In this activity, you’ll be scanning a spinning fidget spinner. Draw a quick sketch of what you think the scan will look like.
Put the spinner on the bed of the scanner or photocopier.
Gently hold the spinner so it doesn’t tip or hit the glass, and then use your other hand to spin it.
While the spinner is still spinning, start a scan.
Look at the picture your scanner or photocopier made. Does it look the way you expected?
Repeat the activity a few times, rotating the spinner faster and slower. Does your spinner always have three blades?

What’s happening?

A scanner is something like a camera, but rather than capturing a whole scene at the same time, it takes lots of long, thin images, and combines them into one big image. If you watch your scanner with the lid open, you can see the camera inside as it moves.

This is a good away to get high quality pictures of something that doesn’t move. But if you try to scan a moving object, the image will look very strange. The top of the image is captured much earlier in time than the bottom, so the image will be smeared and distorted. We can use this to measure the speed of a rotating object.

If the spinner is going fast enough, the blades will move out of the way much faster than the scanner can scan them. You will get a series of long smears, each representing the passing of one blade across the camera. If you work out the time between each smear, it can be used to calculate the rotation speed of the whole spinner.

Speed test (for more advanced mathematicians)

Put the ruler on the bed of the scanner or photocopier, and get your timer ready.
Start a scan, and time how long it takes to complete. Then start another scan and measure the distance the camera moves.
Divide the distance (in centimetres) by the time (in seconds) and you’ll have the speed of the camera in centimetres per second!
Tear off a piece of paper, draw an arrow on it, and lay it on the scanner or photocopier, pointing in the direction the camera moves. This will make it easier to interpret your scans.
Put your fidget spinner on the scanner or photocopier, carefully spin it, and start a scan.
Look at the scan. Hopefully, you have some weird bits that are not attached to the centre of the spinner. If not, spin the spinner a bit faster and make another scan.
When you have a good scan, make sure you have a printed copy so you can draw on it.
Work out which direction the camera moved. Draw a line along the scan in that direction, one that goes straight through the middle of the spinner.
Put your ruler along the line. Measure the distance between the tops of two blobs that are next to each other, in centimetres. There is a picture below to help you understand.
Now divide the distance between blobs by the speed of the camera. This will give you the time it takes for a blade to spin around to the same place.
Not so fast! There are three blades, so it will actually take three times as long. Multiply your time by three and write it down.
Now, calculate the rotation speed in revolutions per minute. Start with 60 seconds, and divide by the rotation time you calculated in the previous step. This will give you the number of full revolutions in one minute. Then multiply by 60 again to get revolutions per hour – this will be a big number!
To calculate distance the tip of a blade travels in one rotation, measure the distance from the centre of the spinner to the end of a blade in centimetres. Then multiply that number by 6.3 (or two times Pi). Convert this distance to metres (divide by 100), and then to kilometres (divide by 1000). Your answer will be a very small number.
Multiply the rotations per hour by the rotation distance in kilometres. You’ll get the speed of the blade tips in kilometres per hour. Congratulations!

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