A rigid, massless rod pivots about a vertical axis. A small point mass is attached to…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A rigid, massless rod pivots about a vertical axis. A small point mass is attached to the rod at a fixed distance from the pivot. Consider the moment of inertia of this single point mass about the axis.
Respond to each part in the spaces provided, using clear reasoning and appropriate physics vocabulary.
(a) Describe how the moment of inertia changes if the distance between the mass and the axis is doubled while the mass itself remains unchanged.
(b) The original mass is now replaced by a new mass that is half as large, but it is positioned at twice the original distance from the axis. Explain whether the moment of inertia increases, decreases, or stays the same compared with the original arrangement, and justify your answer.
(c) A student claims that increasing the mass by a factor of three always triples the moment of inertia, regardless of where the mass is placed. Evaluate this claim, citing specific proportional relationships in your explanation.