A physics research team investigates an unfamiliar rigid object of mass and outer radius

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems

Problem

A physics research team investigates an unfamiliar rigid object of mass

1.2\,\text{kg}

and outer radius

0.15\,\text{m}

. The object rolls without slipping on a level track. Motion sensors measure a center-of-mass speed of

2.6\,\text{m}\,\text{s}^{-1}

and a rotational kinetic energy of

0.41\,\text{J}

about the object’s central axis. (a) Derive a general expression, in terms of the dimensionless constant

k

defined by

I=kMR^{2}

, for the fraction of an object’s total kinetic energy that is rotational when it rolls without slipping. (b) Using the experimental data, determine the numerical value of

k

for the unfamiliar object. (c) Compare your result with standard

k

values for common shapes (solid sphere, solid cylinder, thin hoop) and identify which shape most closely matches the object. Justify your choice.

Related theory

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