A uniform thin rod of mass and length is pivoted about an axis perpendicular to the…

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

Problem

A uniform thin rod of mass

M

and length

L

is pivoted about an axis perpendicular to the rod that passes through a point

P

located at a distance

x

from the centre of the rod (

0 < x < \tfrac{L}{2}

). (i) Derive an expression for the moment of inertia

I_P

of the rod about the axis through

P

in terms of

M, L

and

x

. (ii) Using your result, evaluate

I_P

for

x = \tfrac{L}{3}

. (iii) Comment on the limiting values of

I_P

x \to 0

and as

x \to \tfrac{L}{2}