Yo-Yo Dynamics

This interactive simulator explores Yo-Yo Dynamics in Classical Mechanics. Unwinding string: a = g/(1+I/mr²), T, α, optional friction torque τ. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Classical Mechanics.

Key terms

  • dynamics
  • yoyo
  • mechanics
  • classical

Live graphs

How it works

A yo-yo falls while string unwinds from the small axle of radius r. If the string does not slip on the axle, the center-of-mass speed and angular speed stay locked by v = ωr. Newton’s laws give mg − T = ma and Tr − τ_friction = Iα with α = a/r, so a = g/(1 + I/(mr²)) when τ = 0 — much less than free fall because translational kinetic energy is shared with spin. Larger I or smaller r (larger I/(mr²)) makes the descent slower. A constant opposing friction torque τ at the axle reduces α and a until, if τ ≥ mgr, the yo-yo can hang without accelerating.

Key equations

mg − T = ma  ·  Tr − τ = Iα  ·  a = αr
τ = 0:   a = g/(1 + I/(mr²))  ·  α = (mgr − τ)/(I + mr²)