Scalar Moment of Inertia of A Rigid Body
In mechanics of machines, when designing rotary parts like gears, pulleys, shafts, couplings etc., which are used to transmit torques, the moment of inertia has to be considered. The moment of inertia is given about an axis and it depends on the shape and density of a rotating element.
When considering rotating systems like drive shafts, gear trains, and pulleys with more than one rotating element, more than one axis of rotation, an equivalent moment of inertia for the system can be found. The moment of inertia can be determined experimentally by measuring the angular acceleration for a known torque or it can be calculated from the masses and dimensions of the rotating elements and shafts.
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... The moment of inertia of a part around an axis can be determined experimentally by forming a compound pendulum ... freely in a plane perpendicular to the direction of the desired moment of inertia ... the period of oscillation is measured to be τ = 2π/ω, then the moment of inertia about the pivot point is given by The moment of inertia of the part about the center of mass, IC, is ...
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