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For K-12 Students · Moment of Inertia

Moment of Inertia for a ballistic trajectory

Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a ballistic trajectory live below — adjust the inputs and watch it respond, right in your browser.

Moment of InertiaLive

rotational mass & the parallel-axis theorem

Controls

Shape

Presets

Mass (kg)

Size R or L (m)

Axis offset d (m)

Moment of inertia is rotational mass: how hard it is to spin an object. Mass farther from the axis counts more (∝ r²). The parallel-axis theorem adds md² when the axis moves off the center of mass.

▶ Run in Python

Data Inspector

I about center0.0900 kg·m²

Parallel-axis term0.0000 kg·m²

Total I0.0900 kg·m²

Governing equation

I = 0.500 M R^{2} + M d^{2} = 0.0900 + 0.0000 = 0.0900 kg \cdot m^{2}

Reading this result: The axis runs through the center of mass, so there is no parallel-axis penalty — this is the smallest moment of inertia this body can have.

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Frequently asked questions

Is this good for k-12 students?: Yes — this version of "Moment of Inertia for a ballistic trajectory" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.