The idea of this method is to attach the body to be measured to a long string, forming a physical pendulum. If we plot the left-hand side vs. \(L^{2}\), we will get a straight line of slope \(m\) and ...The idea of this method is to attach the body to be measured to a long string, forming a physical pendulum. If we plot the left-hand side vs. \(L^{2}\), we will get a straight line of slope \(m\) and ordinate intercept equal to the moment of inertia \(I\). Perform a linear regression analysis on the data (treating \(L^{2}\) as the independent variable, and \(T^{2} m g L / 4 \pi^{2}\) as the dependent variable).
where \(I_{p}\) is the moment of inertia of the pulley, \(I_{r}\) is the moment of inertia of the rod, and \(I_{b}\) is the moment of inertia of the test body, which is what we're trying to measure. T...where \(I_{p}\) is the moment of inertia of the pulley, \(I_{r}\) is the moment of inertia of the rod, and \(I_{b}\) is the moment of inertia of the test body, which is what we're trying to measure. The pulley and rod are both disks, so their respective moments of inertia are \(I_{p}=\frac{1}{2} m_{p} r_{p}^{2}\) and \(I_{r}=\frac{1}{2} m_{r} r_{r}^{2}\), where \(m_{p}\) and \(r_{p}\) are the mass and radius of the pulley, and \(m_{r}\) and \(r_{r}\) the mass and radius of the rod.
