The moment of inertia of a slim rod about a transverse crosswise) axis through one end is mL²/3, where m is the mass of the rod and L is its length. The moment of inertia of a 0.24-kg meter stick about a transverse axis through its center is A) 0.14 kg · m². B) 20 kg · m². C) 0.020 kg · m². D) 80 kg · m². E) 4.5 kg · m².

Question

Quizplus · Accepted Answer

The given moment of inertia formula for a slim rod is:
$I = \frac{1}{3} mL^2$
For a meter stick of mass 0.24 kg and length 1 m, the formula becomes:
$I = \frac{1}{3} (0.24	ext{ kg})(1	ext{ m})^2 = 0.080	ext{ kg}\cdot	ext{m}^2$
But this is the moment of inertia about the center axis, not the end. We can use the parallel axis theorem to find the moment of inertia about an axis through one end:
$I_{end} = I_{center} + Mh^2$
Where $M$ is the mass of the meter stick, $h$ is the distance from the end to the center of mass (which is half the length of the meter stick), and we can substitute $I_{center}$ as found above:
$I_{end} = 0.080	ext{ kg}\cdot	ext{m}^2 + (0.24	ext{ kg})(0.5	ext{ m})^2 = 0.020	ext{ kg}\cdot	ext{m}^2$
Therefore, the answer is choice C.

The Moment of Inertia of a Slim Rod About a Transverse