A solid, uniform disk of radius and mass is mounted so that it can spin about an axle…

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A solid, uniform disk of radius

0.15\,\text{m}

and mass

1.8\,\text{kg}

is mounted so that it can spin about an axle that is perpendicular to the plane of the disk and located

0.050\,\text{m}

from the disk’s geometric center. When the disk is set into rotation about this off-center axle, its rotational inertia is measured to be

0.034\,\text{kg}\,\cdot\text{m}^{2}

. Ignore the mass of the axle. (a) Calculate the rotational inertia of the disk about an axle that passes through its center and is perpendicular to the disk. (b) The theoretical expression for a uniform disk’s rotational inertia about a central axle is

I_{\text{th}} = \tfrac{1}{2}MR^{2}

. Determine the percent difference between the value obtained in part (a) and

I_{\text{th}}

. State two plausible experimental factors that could account for any discrepancy.

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