A thin uniform rectangular plate of mass and width is mounted so it can rotate about…

PHYSICS · Subjective · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A thin uniform rectangular plate of mass

M

and width

w

is mounted so it can rotate about an axis parallel to its height and lying in the plane of the plate at a distance

x

from its center of mass. The design requires that the rotational inertia about this axis not exceed

1.5

times the rotational inertia

I_{cm}=\tfrac{1}{12}Mw^{2}

about the central axis parallel to the height. Derive the inequality that limits

x

and determine the maximum allowable value of

x

in terms of

w