A uniform, thin steel bar of length and mass is mounted so that it can rotate freely…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform, thin steel bar of length 0.80m and mass 2.0kg is mounted so that it can rotate freely in a horizontal plane about a vertical axle. Two different axle positions are considered.
• Case A: The axle passes through the midpoint of the bar.
• Case B: The axle passes through a point on the bar that is 0.20m from the midpoint.
Throughout this problem, ignore the mass of any hardware used to attach the bar to the axle.
(a) Without performing a numerical calculation, indicate whether the rotational inertia of the bar in Case B is greater than, less than, or equal to that in Case A. Justify your answer in terms of the distribution of mass relative to each axle.
(b) The axle is moved still farther from the midpoint by a distance d (measured along the bar). Describe qualitatively how the rotational inertia of the bar changes as d increases, and explain why that change depends on the product of the bar’s mass and the square of the shift distance.
(c) Suppose an experimenter measures the rotational inertia of the bar about several different axle positions and plots the results versus d2. Predict the general shape of the graph and explain what physical quantities can be determined from its slope and intercept.