We derive expressions for the exact probability distribution functions and statistical moments of measurements represented as products and quotients of independent random variables, test these relations by means of the α and β branching decays of Bi212, and discuss the implications of our theory for the measurement of lipid-panel analytes in the assessment of the risk of coronary heart disease.
A physical pendulum consisting of a circular disk at the end of a thin metal rod is connected to a low-friction rotary motion sensor, so that its angular position and velocity can be accurately measured. The disk can be oriented either perpendicular or parallel to the plane of swing to give significant or negligible air drag, respectively. The motion is analytically modeled in phase space. A quadratic dependence of the damping torque on the angular velocity fits the results. This laboratory experiment is suitable for undergraduate physics majors taking a first or second course in classical mechanics.
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