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For Students · Rolling Without Slipping

Rolling Without Slipping for a car braking

Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a car braking live below — adjust the inputs and watch it respond, right in your browser.

Rolling Without SlippingLive

a shape race down the ramp

Controls

Presets

Incline angle (°)

All these shapes share the same mass and radius, yet a solid sphere beats a hoop every time. Acceleration = g·sinθ / (1 + I/mR²): mass concentrated near the axis (small I) accelerates faster — and the result is independent of mass and radius.

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Data Inspector

Hoop accel1.12 m/s²

Disk accel2.24 m/s²

Sphere accel2.40 m/s²

Shell accel2.01 m/s²

Governing equation

a = \frac{g sin θ}{1 + I / m R ^{2}} = \frac{9.81 sin 2 0 ^{\circ}}{1 + I / m R ^{2}} = \frac{3.36}{1 + I / m R ^{2}} m/s^{2}

Reading this result: At 20° the solid sphere leads at 2.40 m/s² while the hoop trails at 1.12 m/s² — a 2.14× gap fixed entirely by mass distribution, independent of the incline and of every shape mass and radius.

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Frequently asked questions

Is this good for students?: Yes — this version of "Rolling Without Slipping for a car braking" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.