We’re trying to find the frequency at which a gear on a fidget toy is spinning. Firstly, the centres of each gear form a hexagon shape. Since each gear has radius 10 centimetres, this hexagon has side length 20 cm. In a hexagon, the distance between two opposite vertices is double that of the side length. So the outermost gear is 40 cm from the innermost. Centripetal force is π2rλ/s inwards. r is the distance between the point that’s moving and the point it’s moving around. λ is the frequency at which it is moving around. We can move around the elements around to see that λ = Fs/π2r, where F is centripetal force. Plug in the knowns to see that the gear is moving around 0.2533 times per second. If you tried making the device, you’d see that only three gears spin. That’s because, for the anchored gear to stay in position, the motion of the hexagon has to exactly balance it’s rotation. That means 2 other gears will be balanced, but the other 3 will move at double speed. Half from the rotation of the hexagon and half from their own rotation. So the rotation from the hexagon, 0.2533 rotations equals that at which the gear is spinning. Therefore the gear is moving at 0.2533 rotations per second.