Mass moment of inertia, abbreviated as I, also called rotational inertia, is a property of a body that measures its resistance to a change in its rotational motion. Just as an object's mass resists a change in its linear motion (according to Newton's Second Law), the mass moment of inertia resists a change in its angular motion when a torque is applied. The relationship is similar, the torque applied to a rigid body is equal to its mass moment of inertia multiplied by its angular acceleration.
Mass Moment of Inertia Formula |
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\( I \;=\; k \cdot m \cdot \bar r^2 \) (Mass Moment of Inertia) \( k \;=\; \dfrac{ I }{ m \cdot \bar r^2 } \) \( m \;=\; \dfrac{ I }{ k \cdot \bar r^2 } \) \( \bar r \;=\; \sqrt{ \dfrac{ I }{ k \cdot m } }\) |
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| Symbol | English | Metric |
| \( I \) = Mass Moment of Inertia | \(lbm \;/\; in^2\) | \(kg \;/\; mm^2\) |
| \( k \) = Internal Constant (Depends on the Shape of the Object) | \(dimensionless\) | \(dimensionless\) |
| \( m \) = Mass | \(lbm\) | \(kg\) |
| \( \bar r \) = Distance Between Axis and Rotating Motion | \(in\) | \(mm\) |
The mass moment of inertia depends on two key factors, the total mass of the body and how that mass is distributed relative to the axis of rotation. The farther the mass is from the axis of rotation, the greater the mass moment of inertia will be, and the more torque will be required to change its angular velocity. For a simple point mass, the formula is \(I = m \cdot r^2\), where \( is the mass and \( is the distance from the axis of rotation. This concept is crucial in fields like mechanical engineering and physics for analyzing the rotational dynamics of objects, from flywheels and gyroscopes to planets.
