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The Moment of Inertia Calculator will calculate:

- Moment of Inertia of a bar rotating around its centre
- Moment of Inertia of a bar rotating around its end
- Moment of Inertia of a cylinder or disc rotating around its axis of symmetry
- Moment of Inertia of a cylinder or disc rotating around its central diameter
- Moment of Inertia of a ring rotating around its axis of symmetry
- Moment of Inertia of a ring rotating around its diameter
- Moment of Inertia of a sphere rotating around its diameter
- Moment of Inertia of a spherical shell rotating around its diameter
- Moment of Inertia of a point object rotating around a given axis

The Moment of inertia of a bar rotating around its centre calculation is kg∙m^{2} |

The Moment of Inertia of a bar rotating around its end is kg∙m^{2} |

The Moment of Inertia of a cylinder or disc rotating around its axis of symmetry is kg∙m^{2} |

The Moment of Inertia of a cylinder or disc rotating around its central diameter is kg∙m^{2} |

The Moment of Inertia of a ring rotating around its axis of symmetry is kg∙m^{2} |

The Moment of Inertia of a ring rotating around its diameter is kg∙m^{2} |

The Moment of Inertia of a sphere rotating around its diameter is kg∙m^{2} |

The Moment of Inertia of a spherical shell rotating around its diameter is kg∙m^{2} |

The Moment of Inertia of a point object rotating around a given axis is kg∙m^{2} |

Moment of inertia of a bar rotating around its centre calculation |
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I = × m1/12_{b} × L^{2}I = × 1/12 × ^{2}I = × × I = |

Moment of inertia of a bar rotating around its end calculation |

I = × m1/3_{b} × L^{2}I = × 1/3 × ^{2}I = × × I = |

Moment of Inertia of a cylinder or disc rotating around its axis of symmetry calculation |

I = × m1/2_{C} × R_{C}^{2}I = × 1/2 × ^{2}I = × × I = |

Moment of Inertia of a cylinder or disc rotating around its central diameter calculation |

I = m1/4_{C} × R_{C}^{2} + m1/12_{C} × h^{2}I = 1/4 × ^{2} + 1/12 × ^{2}I = × × + × × I = |

Moment of Inertia of a ring rotating around its axis of symmetry calculation |

I = m_{R} × R_{R}^{2}I = × ^{2}I = × I = |

Moment of Inertia of a ring rotating around its diameter calculation |

I = m1/2_{R} × R_{R}^{2}I = 1/2 × ^{2}I = × × I = |

Moment of Inertia of a sphere rotating around its diameter calculation |

I = m2/5_{S} × R_{S}^{2}I = 2/5 × ^{2}I = × × I = |

Moment of Inertia of a spherical shell rotating around its diameter calculation |

I = m2/3_{Sh} × R_{Sh}^{2}I = 2/3 × ^{2}I = × × I = |

Moment of Inertia of a point object rotating around a given axis calculation |

I = m_{obj} × r^{2}I = × ^{2}I = × I = |

Moment Of Inertia Calculator Input Values |

Mass of bar (mb) kg |

Length of bar (L) m |

Mass of cylinder or disc (mC) kg |

Radius of cylinder or disc (RC) m |

Height of cylinder (h) m |

Mass of ring (mR) kg |

Outer radius of ring (RR) m |

Mass of sphere (mS) kg |

Radius of sphere (RS) m |

Mass of spherical shell (mSh) kg |

Radius of spherical shell (RSh) m |

Mass of the point object (mob) kg |

Distance of the point object from the rotation axis(r) m |

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each moment of inertia calculation, the Moment Of Inertia Calculator will automatically calculate the results and update the Physics formula elements with each element of the moment of inertia calculation. You can then email or print this moment of inertia calculation as required for later use.

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I = *1**/**12* × m_{b} × L^{2}

I = *1**/**3* × m_{b} × L^{2}

I = *1**/**2* × m_{C} × R_{C}^{2}

I = *1**/**4*m_{C} × R_{C}^{2} + *1**/**m*12_{C} × h^{2}

I = m_{R} × R_{R}^{2}

I = *1**/**2*m_{R} × R_{R}^{2}

I = *2**/**5*m_{S} × R_{S}^{2}

I = *2**/**3*m_{Sh} × R_{Sh}^{2}

I = m_{obj} × r^{2}

The following Physics tutorials are provided within the Rotation section of our Free Physics Tutorials. Each Rotation tutorial includes detailed Rotation formula and example of how to calculate and resolve specific Rotation questions and problems. At the end of each Rotation tutorial you will find Rotation revision questions with a hidden answer that reveals when clicked. This allows you to learn about Rotation and test your knowledge of Physics by answering the test questions on Rotation.

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