Moment of inertia
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Definition of inertia for a particle
Equations are omitted for technical reasons - download the original pdf
Let P be a particle of mass m rotating about an axis at a distance r. Then the moment of inertia I, of P about this fixed axis is given by [Equation goes here - download the original to see it.] We will now demonstrate the consistency of this definition. [Diagram goes here - download the original to see it.] Let P be rotating about a fixed axis L passing through a point O at a distance r from P. Let its angular acceleration about this axis be [Equation goes here - download the original to see it.] Its linear acceleration may be resolved into two components - one radial, FR, and the other tangental, FT, to the orbit. [Diagram goes here - download the original to see it.] The linear acceleration of the object can likewise be resolved into radial and tangental components. Radially, the linear acceleration is a centripetal acceleration and is given by: [Equation goes here - download the original to see it.] Tangentally, the linear acceleration is given by: [Equation goes here - download the original to see it.] is arc length. That is tangental linear acceleration is [Equation goes here - download the original to see it.] [Diagram goes here - download the original to see it.] Tangental linear acceleration must obey Newton's Second law, hence: [Equation goes here - download the original to see it.] Multiplying both sides by r: [Equation goes here - download the original to see it.] But [Equation goes here - download the original to see it.] is the torque (or moment) applied to P. Hence [Equation goes here - download the original to see it.] Where I = mr2 is the moment of inertia.
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Contents of
Moment of inertia
1 Moment of Inertia
2 Definition of inertia for a particle
3 Addition law for moments of inertia for two or more particles rotating about the same axis of rotati
4 Standard results for moments of inertia
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