A uniform rectangular aluminum plate of mass has length (long side) and width
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform rectangular aluminum plate of mass 4.0kg has length 0.40m (long side) and width 0.30m. It is pivoted so that it can rotate freely about axes that are perpendicular to the plate and lie in its plane.
An experimenter drills small holes along the plate’s width (the 0.30m dimension) and measures the rotational inertia about each hole using a torsion pendulum technique. Two of the measurements are given below.
• Axis P: located 0.12m from the plate’s center along the width. Measured IP=0.080kg⋅m2
• Axis Q: located 0.24m from the plate’s center along the same line. Measured IQ=0.130kg⋅m2
(a) From the measurement at axis P, determine the rotational inertia of the plate about an axis perpendicular to the plate and passing through its center.
(b) Use the plate’s dimensions to calculate the theoretical rotational inertia about the central perpendicular axis. Clearly state any formula you employ.
(c) Compute the percent difference between your answers to parts (a) and (b). Evaluate the consistency of the experimental result with theory.
(d) Using the data for axes P and Q, explain how one could graphically test whether the rotational inertia depends linearly on the square of the distance between the chosen axis and the plate’s center. State what physical quantities would correspond to the graph’s slope and intercept.