Why does a larger disk radius R change the acceleration?

For fixed axle r, increasing R raises I = ½MR², so more energy goes into rotation per meter fallen and linear acceleration drops.

Is string mass included?

No. The model assumes a light string and ideal no-slip on the axle.

Maxwell wheel (yo-yo disk)

Disk on a thin axle unwinds string: shared linear and rotational kinetic energy from falling potential, a ≈ g / (1 + I/(mr²)).

About this model

A Maxwell wheel (yo-yo disk) converts gravitational potential into both translational motion of the center and rotation about the axle as string unwinds. With no slip between string and axle, v = ωr_axle and energy splitting yields linear acceleration a = g / (1 + I/(M r²)) for the center-of-mass speed when I is taken about the center. The demo uses I = ½MR² for a solid disk about its center; string wraps on the small axle radius. A simple bounce at the bottom is stylized, not an elastic collision with a real floor.

Who it's for: High school through intro college energy/work rotation topics.

Key terms

Maxwell wheel
Rolling constraint
Moment of inertia
Energy sharing
Yo-yo equation

How it works

A heavy disk on a thin axle unwinds string from the axle: translational and rotational kinetic energy share the loss in gravitational potential. Model uses no-slip v = ω r_axle and I = ½MR² for the disk about its center.

Frequently asked questions

Why does a larger disk radius R change the acceleration?: For fixed axle r, increasing R raises I = ½MR², so more energy goes into rotation per meter fallen and linear acceleration drops.
Is string mass included?: No. The model assumes a light string and ideal no-slip on the axle.

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