A uniform thin rod of length is pivoted at a point located at a distance from one end

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

Problem

A uniform thin rod of length

L

is pivoted at a point

P

located at a distance

\dfrac{L}{4}

from one end. The axis is perpendicular to the rod and passes through

P

. (i) Obtain an expression for the moment of inertia of the rod about the pivot axis in terms of

M

and

L

. (ii) Hence derive the corresponding radius of gyration

k_{P}

. (iii) Express

k_{P}

as a fraction of the rod length

L