Rolling Race: Hoop vs Disc vs Sphere

Release three objects together on identical inclines. Compare how rotational inertia changes their acceleration and finish time.

Hoop acceleration1.27 m/s²

Disc acceleration1.69 m/s²

Sphere acceleration1.81 m/s²

Fastest objectSolid sphere

Race time0.00 s

Race setup

Incline angle, θ 15°

A steeper incline increases all three accelerations.

Track length, s 5.00 m

All objects travel the same distance along the incline.

Object radius, R 0.30 m

For ideal rolling, changing R does not change the winner.

a = g sinθ / (1 + I/mR²)
Hoop: I = mR² | Disc: I = ½mR² | Sphere: I = ⅖mR²

Prediction: The object with the smallest rotational-inertia factor uses less of its gravitational energy in rotation and gains translational speed fastest.

Race

hoop: β = 1 solid disc: β = 1/2 solid sphere: β = 2/5

Sphere

2.35 s

Disc

2.43 s

Hoop

2.80 s

Hoop Translational KE: 50.0% Rotational KE: 50.0%

Solid disc Translational KE: 66.7% Rotational KE: 33.3%

Solid sphere Translational KE: 71.4% Rotational KE: 28.6%

Predict before changing a control

Make the incline steeper. Does the finishing order change?