Math and Yo-Yo’s

Follow as Andrew and Hawthorne Yo-Yo our way through math using yo-yo’s to help us show the relations of position, velocity and acceleration.

Webster’s Dictionary defines a Yo Yo as  a round toy that has two flat sides with a string attached to its center, that is held in your hand, and that is made to go up and down by unwinding and rewinding the string with a movement of your wrist…….. But is it really just that?


  • That the X Position graph of each yoyo is the antiderivative of the yoyo’s  X Velocity graph, and the X Velocity is the derivative of the X Position.


  • That the X Acceleration graph of each yoyo is the derivative of each yoyo’s velocity graph.
  • Each yoyo although similar, have very slight differences in their stats even when performing the same tricks at the same string lengths.



  • We first took videos of Yo-Yo champion Andrew doing yo yo tricks.
  • We then downloaded software that allows us to track an object throughout the video (the program is “Tracker”), which then produced a graph of position, velocity, and acceleration for both X and Y values.
  • Using the different graph settings we are able to prove that the position, velocity, and acceleration are all derivatives of each other.


yo yo


First Trick: