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Mathematically, the moment of inertia ''I'' for a mass ''m'' that is moving a perpendicular distance of ''r'' from an axis is expressed as:
 
Mathematically, the moment of inertia ''I'' for a mass ''m'' that is moving a perpendicular distance of ''r'' from an axis is expressed as:
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:<big><big><math>I = \int r^2 \,dm</math>
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:<big><big><math>I = \int r^2 \,dm</math></big></big>
    
The formula for a moment of inertia is the result of combining the equation for [[kinetic energy]] with the equation for angular velocity.
 
The formula for a moment of inertia is the result of combining the equation for [[kinetic energy]] with the equation for angular velocity.
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