A Simple Moment of Inertia Measurement

Modern MEMs gyros/accelerometers allow the angular velocity of pendula to be precisely measured and the angular acceleration to be calculated. For a compound pendulum, Ipθ¨=−mgasinθ, where a is the distance of the center of mass from the pivot, so the moment of inertia Ip of the compound pendulum about the pivot can be simply derived as Ip=−mga/θ¨(θ=π/2) from measurements of the angular acceleration θ¨(θ=π/2) when the pendulum is horizontal. Then mga can be determined by measuring the force and lever arm required to maintain the pendulum in a horizontal position.